[[460, 116, 3]] magic-state factory, T0·T1·T2·T3·T4·T5·T6·T7·T8·T9·T10·T11...

The circuit

The 128\times460 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.

output wires
check wires, measured and postselected

wire	0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| '
out 0 (183)	·1····111··1····1········1···11·111···111·1··1·····11·1·111··1··1···1·····1··1·11·····11···1··1·····1·111111·1··1·1·1··11···111·1··1·1·1·1·1·11·11·····11111···1····1·1······11·1··1··1··1··1···1··11·1·11·11·1·1·111··11····1·1···1·····11··1·1·····1············1···11··11·1···111·1··1··1·1·1·11·1···1···1·1····1·1·11······11····1·1·····1·11111·1·1··1·1···11·1··1·1·1···1·1·1·1·1·1···1·11··1·11·11···1···11···11·1···1··1··1··1···1···111·11·11··1·1··111··1·1·11····
out 1 (175)	111····1·1·1····1·1····1·1·1·1··1··11·····1··1·····11·1·1··1·111·1···11···1···1·1···11·1·1·1········1·111111·11··1·1·1···1···11·1····1·1·1·1·····1···1···11·111·1···1·1·······1··1111··1·111·111·1···1·1······1···1·1··11····1·1··111·····1···11·····1·1········1·1·1·1···1···1·1····1··1··1·1·1·1···1··111··1·11··1··1·1···1·1·1··1·1·······1·11111·1·1·1·1·11···1···1·1·1·····1·1·1·1········11····1·1·111·1··11····1··11·11··1·111·111·1·····1·······1····1·1··1·1·11····
out 2 (159)	····1······11·1···1·1··1111·111··111············1·11111··1111·······11·······11·1···1····1····1····11111111······111·1111····1·····1·111····1·1·1····1·······1111·····1·1····1··1········11····111··1·····111···1·1·11··················1······111·····1···1····1111·111···1·11··········111·111··1·11·1······11·····11·1···1······1···1····11111111·······1111111····1·······1·111····1····1·1·1·········1111···1·1·1··1·········11····111·1·1····111····1··1·11···········
out 3 (167)	·1··1···1··1····1········1·1·11·111···11··1··1·····11·1·1·1··1··1···1·1······1·11···1·11···1···1····1·111111·1··1·1···1·1···11··1··1·1·1·1·1·1··11·····111·1···1····1·1·······1·1··1··1·····1·1·1··11·1·1··11·1·1·1····11····1·1···1····1····1·1··1··1············1·1·11··11·1···11··1··1··1·1·1·1··1···1···1·1·1····1·11···1··11····1··1····1·11111·1·1··1·1··1·1·1··1···1···1·1·1·1·1·1·····11··1·11··1···1···11····1·1···1··1·····1·1·1···111·1··11··1·1··1····1·1·11····
out 4 (183)	1·1······1··1·1··11·1····1·1·11·111···111····1·····11·1·1·1·11·11···1·1······11···1·1·····1·1·11····1·111111·1···1·1·1·1·1·····1·1·11·1··1·1·1··11·····11111·1·1····1·1·······1·11····1····1·1·1·1·1···1·11·11·1····11·11····1·1··1·1·········1·11····11···1······1·1·11··11·1···111····1··1·1·1·1··1··11·1·1·1·1····11··1··1·······1·111····1·11111·1·1···1·11·1·1······1·1··11·1··1·1·1·····11··1·11·11·1·1···11····1·11·····1····1·1·1·11·1··1·11·1·1·1·····11·1·1·11····
out 5 (175)	·1··1···1··1···1111······1·1·11·111···11··1··1·····11·1·1·1··1··1···1·1······1·11······1···1··1·····1·111111·1··1·1···1·1···111·111··1·1·1·1·1··11·····111·1···1····1·1·······1·1··1··1·····1·1·1··11·1·11·1··1·1·111··11····1·1···1····1····1·1·····111··········1·1·11··11·1···11··1··1··1·1·1·1··1···1···1·1·1····1·11·······1····1·1·····1·11111·1·1··1·1··1·1·1··1·1·11·1··1·1·1·1·1·····11··1·11··1···1···11····1·1···1··1·····1·1·1···111·11·1···1·1··111··1·1·11····
out 6 (175)	·1··1··11··1····1········1···11·111····1··1··1·····11·1·1·1··1··1···1·····1··1·11···1·11···1··11····1·111111·1··1·1···111···111·1··1·1·1·1·1·11·11·····11··1···1·1··1·1·······1·1··1··1··1··1···1··11·1·1··11·1·1·11···11····1·1···1····1·1··1·1·····1············1···11··11·1····1··1·11··1·1·1·1··1···1···1·1····1·1·11···1··11····1·11····1·11111·1·1··1·1··111·1··1·1·1···1·1·1·1·1·1···1·11··1·1···1···1·1·11····1·1···1··1··1··1···1···111·1··11··1·1··11···1·1·11····
out 7 (159)	·1·····11··1·····1··1···1·111···111·1···1·1··1··1·1··1··1·1··11··1··1····1····1·1····1····1·1······1·1·····1·1··11·1·1······11·1·1··11·1·1·11·1··1·······1··1··1····1···1·····1·1·1·1··1·1··1111·1····1·11···1·1··1·1··11····1·1···1······1··1·1······1····1·····1·111····11·1··1··1·1··111···1··1··1···11···11···1···1·1·····1·····1·1·····1·1······1·1··11·11····1··1··1·1···11·111·11····1··1·····1···1··1···1··1··1·1·1··1··1·1··1111·1····1·11····1·1···1·1··1·1·11····
out 8 (183)	·1····1111·11·1··11·······11111111111···1···········11111·111·1·······1··1····111·1·11·1······11··1··1··1111111······1··11··11111111·············1···1·1111·············1····11·1·111····1···1······1·111·1·1111···11······1·1··1··1·····11··11111····11···········11111·111·11·1··1·········11111··11·1·1······1·1···1111··1·1·1······11·1···1··111·111·1····1··111··1·1111·11················11·1·11·1···········1·11·1·1·11····1···1·······1111·1·1·111····11···1·11··1··
out 9 (175)	·1··1··1···11·1··1··1···111·11···111·11·········1·11111··1111··1····111··11··111····11········1····11111111···1··111·11·1····1····1··111····111······1··11···1111·····1·1····1··1··1······1··11111·11·····1·1·····1·11·············1····1·1····111····1····1·····111·11····1·11··1·······111·111··1·11·1··1···111·11·111····1·1········1····11111111·····1·11111·1····1······1··111····11···1···1···11····1111···1·1·1··1···1······1··11111··11····1·1·······1·11···········
out 10 (31)	·······1··········1······1············1··················1············1···1···········1································1···········1·····················1···················1···········1····1·············1·····························1············1··········1··············1················1·············1··1···········1································1·············1···········1··········1···············1············1····1·············1······················
out 11 (167)	111·····11·11·1···1·1···111·11······1·111·1··1··1·11111·····111111····1··1······1·1·1·········11···11111111·····1········1··11·····1·111····111········11··111····1···1·1········1··1·11·1·11·1····1··111·111·····1··1············111········11111·····1···1·····111·11·········1111·1··1111·111·······1111·11··1·1·····11··1··········11···11111111······1·······11··1·······1·111····11···1·····1·1···111······1·1·····1···1·11·1·11·1·····1·111·111·······1··1···········
out 12 (175)	·1··1···1··1····11·······1·1·11·111····1·11··1·····11·1·1·1·11··1···1········1·11·····11···1··11····1·111111·1··1·1···1·1···111·1·11·1·1·1·1·1··11·····11······1····1·1·······1·11·1··1··1··1·1·1··11·1·11·11·1·1·11···11····1·1···1····1····1·1·····11···········1·1·11··11·1····1··1··1··1·1·1·1··1··11···1·1······1·11······11····1·11····1·11111·1·1··1·1··1·1·1··1·1·1··11·1·1·1·1·1·····11··1·1·······1···11····1·11··1··1··1··1·1·1···111·11·11··1·1··11···1·1·11····
out 13 (167)	·1··1···1··1····1·1······1·1·11·111····11·1··1·····11·1·1····1··1···1········1·11···1··1···1··11····1·111111·1··1·1···1·1···111·1····1·1·1·1·1··11·····11·11···1····1·1·······1·1··1··1··1··1·1·1··11·1·1··1··1·1·11···11····1·1···1····1····1·1·····1·1··········1·1·11··11·1····11·1··1··1·1·1·1······1···1·1······1·11···1···1····1·11····1·11111·1·1··1·1··1·1·1··1·1·1·····1·1·1·1·1·····11··1·1··11···1···11····111···1··1··1··1·1·1···111·1··1···1·1··11···1·1·11····
out 14 (199)	111·1·1·1···1·1········11··1·111·11·1·111····1··1·1·1·11··1·11111····11··11··11·····11·1·11·1······1·1·1111·1·1···1··111····1·1·1·1·11·1·1·111············11··1·1···1········1··11111·1··111··1·1··1··1·11111·1·1·1·1··11····1·1··111···11···1··11··············11··1·11·1·1·1··1111····111··1·11···1··1111·1··11·11·11·····1·1·1··11·1·····1·1·11111·1··1··1·111··1····1·1··1·11·1·1·111··············11··1·1··1····1··111·11·1··111··1·1···1·1·11111··1·1··1·1··1·1·11····
out 15 (143)	1·1·1···11·······11··············1111··1··1···············11·11·11··11····1··1111·1···········11··············1·11·1·11111··1·····11·················1·111111·111···············11·11·11·11111·111··1·111··········11·············1·1·1·1····11·······11···················1·11·1·1··1··············11··11··1111···1·11111·············11················111·1111111·········11·················1·1·11·111·111··········11··11·11·11111·111···1111············11············
out 16 (175)	1·1······1··1·1··11·1····1···1··111···11··1··1·····11·1·1·1·11·11···1·1··1····1···1·11····1·1·11····1·111111·1···1·1·1·1·1·····1·1·11·1··1·1·11··1·····111·1···1····1·1·······1·11····1····1···1·1·1···1·11111······11·11····1·1··1·1·········1·11····11···1······1···1···11·1···11··1··1··1·1·1·1··1··11·1·1·1·1·1···1··1··1·1···1·1·111····1·11111·1·1···1·11·1·1······1·1··11·1··1·1·1···1··1··1·11··1···1···11····1·11·····1····1···1·1··1··1·1111·1·······11·1·1·11····
out 17 (175)	····1·1·1··1····11·······1·1·11·111···111····1·····11·1·1·1·11·11···1·1···1··1·111··1··1···1········1·111111·11·1·1·····1···111·1·11·1·1·1·1·1··11·····11111·1·1····1·1·······1·11····1·····1···1··1··1·1··1··1·1·1·1··11····1·1········11···1·1·····11···········1·1·11··11·1···111····1··1·1·1·1··1··11·1·1·1·1··1·1·11···1···1····1·······1·11111·1·1·11·1····1·1··1·1·1··11·1·1·1·1·1·····11··1·11·11·1·1···11····1·11·····1·····1···1···1·1·1··1···1·1··1·1··1·1·11····
out 18 (159)	·1······1·11·····11·····1·1·1·1·111·1········1··1·1··1··1·1··11··1··1····1····1·1····1····1·1······1·1·····1·1··11·1·1·1·····1·1·1·111·1·1·11···11·······11·11·1····1···1·····1·1·1·1··1·1··1111·1····1·11···1·1··1·1··11····1·1···1·········1·1······11·········1·1·1·1··11·1··1·······111···1··1··1···11···11···1···1·1·····1·····1·1·····1·1······1·1··11·11·1·····1··1·1··111·1·1·11······11·····1·1·11·1···1··1··1·1·1··1··1·1··1111·1····1·11····1·1···1·1··1·1·11····
out 19 (183)	·11·1·111··1····1········1·1·1··111···111·1··1·····11·1·111·11·11···1·····1··1·11·····11·1·1········1·111111·1·11·1····11···111·1··1·1·1·1·1·1···1·····11111···1····1·1······11·11····1··1··1···1··11·1·11·11·1···1·1··11····1·1···11···111··1·1·····1············1·1·1···11·1···111·1··1··1·1·1·11·1··11·1·1·1····1·1·11······11··1·1·······1·11111·1·1··1·1···11·1··1·1·1···1·1·1·1·1·1······1··1·11·11···1···11···11·11·····1··1··1···1···111·11·11··1····1·1··1·1·11····
out 20 (175)	111····1·1·1····1·1······1·1····1··11·1·1·1··1·····11·1·1··1·111·1···11··11···1·1·1··1·1·1·1···1····1·111111·11··1·1·1···1···11·1····1·1·1·1·1···1···1······111·1···1·1·······1··1111··1·111··11·1·····1·1····1···1····11····1·1··111·····1···11·····1·1··········1·1·····1···1·11·1·1··1··1·1·1·1···1··111··1·11·11··1·11····1·1··1·1··1····1·11111·1·1·1·1·11···1···1·1·1·····1·1·1·1·1····1·11········111·1··11····1··11·11··1·111··11·1·····1·1·····1····1····1·1·11····
out 21 (31)	······1··········1·········1············1················1············1············1···········1······················1···········1···········1···········1··················1···········1·············1············1····················1············1·············1··············1··············1·············1·······················1······················1·············1··············1··········1·············1············1·············1··············1············
out 22 (183)	····1·11········111·····111111······1·111·1·····1·11111··1····1111····1··11··111····1111·1111·1····11111111······111·1··1·····1111··1····1··11·········11··111········1·1····1····1·1·11·1···11111·11····1·11111···1····················111··········111·····1···111111·········1111·1···111·111··1······11·11··1·11·111····1·111··11111····11111111·······1111··1······1111···1····1··11·········1·1···111······1·1·1····1··1·11·1···11111··11···1·11·111····1·············
out 23 (175)	·1··1··1···11·1···1·1··1111·111··111··1···1·····1·11111···1111······111···1··1111···111··1····1····11111111···1··111·11·1····1·····1·111····1·1·1····1···1····111·····1·1·····1·1·1·······1···1111··1·····1·····1·1·11·············1····1·1····111·····1···1····1111·111···1·11··1···1···111·111···111·11·····111··1·1111···1·11···1···1····11111111·····1·11111·1····1·······1·111····1····1·1·1····1·····111···1·1··1·1·1········1···1111···1····1······1··1·11···········
out 24 (175)	1·1·1··1·1··1·1·11··1··11·1·1···111·1··1··1··1··1·1··1··1·1·111··1··1·1···1··1·11·1····1·1·1·······1·1·····1·1····1···1111····1·1·11··1··1·111···1·······11·1··1····1···1·····1·111·1··1···1·11·1··11··1··1·1·1····1·1·11····1·1··1·1···1·1···1·11···11····1····11·1·1····11·1··1·1··1··111···1··1··1··111···11·1··1·1·111······1··1·1······1·1······1·1····1··1111·····1·1··11··1··1·111······1·····111·1··1···1··1··1·111··1··1···1·11·1···11·1··1·1··1·····1·1·1·1·11····
out 25 (31)	·······1··········1···········1···········1··············1············1·······1··········1·····························1···········1············1············1···············1···········1········1·············1·························1············1···············1·············1············1·············1·····1············1····························1·············1···············1···········1··········1············1·······················1·················
out 26 (183)	1·1···1··1··1·1···1·1····1···11·111···11·····1·····11·1·111····111··1·1···1···1·1·1···1···1·1··1····1·111111·1···1·1·111·1·····1·1111·1··1·1·11·11·····111·1·1·1····1·1······11·1·1··11····1·111·1·····1··1··1·1···111·11····1·1··1·1····1····1·11·····1···1······1···11··11·1···11·····1··1·1·1·11·1·····1·111·1··1··1·11·····1····1·1·1····1·11111·1·1···1·1111·1······1·1·111·1··1·1·1···1·11··1·11··1·1·1···11···11·1·1····1····1·111·1·····1··1···1·1····111·1·1·11····
out 27 (159)	1·1·1···11·11·1·1·1·1··1···1··1·······1··················1··11········1··1···111··1···11··111·················1·1111·11111··1111111·111······11·1········1···················1···11······1·11·1111·11·111111·1111·1111············1·1···1····11111···1·1··11····1···1··1·········1················1····11·······1·1··111·1·····11···111··················11111111111··1·1111·1·111······1···1·1······1···············1···11·······1·11·1111··11111111··1111··1111···········
out 28 (175)	·11····11··11···1···1·······11···1····11··1·····1····1111111···111····1···1·······1·111··11···1···111·11·111··1·111·····11······111····1··1111··11···1··1·1··1·11··11·1······1······1·····1··1·11··11·1···111·11···111··1···11··1··11·····1··1·11····1·····1·········11····1·····11··1···1····11111·11····1·11··1··1·····1··1·11···11··1··1·11·11·11·1···1111····11·······11·1····1··1111·····111···1··1··1·11·111···1·······1·····1··1·11···111···111··11····111···1·1··1··
out 29 (175)	111······1·1····1······1·1···1··1··11···1·1··1·····11·1·11·1·111·1···1···1····1·1·1··111·1·1···1···1111·1·11·11··1·1·1·1·1···11·1··1·1·1·1·1··1··1···1···1··111·1···1·1······11··1111··1··11···1·1·····1·1··1·1···1····111·1······111·········11·····1··········1·1···1···1···1·1··1·1··1··1·1·1·11··1··111··1·1··1···1·11····111··1·1··1···1111·1·1·1·1·1·1·11·1·1···1·1·1···1·1·1·1·1·····1··11····1···111·1··11···11··11·11··1··11···1·1·····1·1··1··1····1····1·11······
out 30 (175)	······111···1·1·11··1···1·111···1··1···11·1··1··1·1··1··1··1·1·11····1········1·····1111·1·1··1····1·1·····1·11·11·1·11·····1·1·1·11··1··1·11·1··1···1·11·11·1111···1···1·····1··1····1···1·1·11·1·1··1·1111··1······1·11····1·1·········11··1··11···11····1·····1·111····1···1···11·11·111···1··1···1··1·1·1··1······1·····1·111··1·1·1····1·1······1·1·111·111···1····1·1··11··1··1·11····1··11·1·1··11·1111··1··1··1··1·····1···1·1·11·1··1·1·1111···1·······1·1·1·11····
out 31 (159)	····1··1···11·1·····1··1111·11···111······1·····1·11111···111·······111··11··1111···111··11···1····11111111······111·11·1····1·······111····1·1······1········111·····1·1·······1·········1··11111··1·····1·····1·1·11··················1·1····111·········1····1111·11····1·11······1···111·111····11·1······111·11·1111···1·11···11··1····11111111·······11111·1····1·········111····1····1···1··········111···1·1····1··········1··11111···1····1······11·1·11···········
out 32 (55)	·1·1···1··········1····1··············1··················1···1·1······1···1·········111·······················1·1······1···········1·········1···········1···················1····11·····1····1··········1·11······················1······1············1········1················1················1·····1·1·····1··1········1·11·························11·····1·············1·········1············1···············1····1·1·····1····1··········1·11······················
out 33 (151)	1·1·1·1·11·······11····1···1·····1111··1··1···············11·11·11··111···1··1111·1··1········1···············1·1111·1·111··1·····11·········11······1·111111·111················1·11·11··1111·111··1·111··1·······1··············1·1···11···11·······11········1···1······1·11·1·1··1··············111·11··11111··1·11111····1········1·················111111·1111·········11·········1···1···1·1·11·111·111···········1··11·11··1111·111···1111··1·········1·············
out 34 (175)	1·1·1··1·1··1·1·11··1··11··11···111·1···1·1··1··1·1··1··1·1·111··1··1·1··1···1·11·1··111·1·1·······1·1·····1·1····1···1111····1·1·11··1··1·1111··1·······1··1··1····1···1·····1·111·1··1···1····1··11··1··11··1····1·1·11····1·1··1·1···1·1···1·11···11····1····11··11····11·1··1··1·1··111···1··1··1··111···11·1·1··1·111····111··1·1······1·1······1·1····1··1111·····1·1··11··1··1·111··11··1·····1···1··1···1··1··1·111··1··1···1····1···11·1··11···1·····1·1·1·1·11····
out 35 (159)	1·1·1··11··11·1·1···1··1··············1·1·1··············1··11········1···1··111··1··1·1··111·················1·1111·11·11·1111111111111·····1···········11··1···············1···11······1·111·111·11·11111·11111·1111············1·1···1·1··1·111···1·····1····1················1·1·1············1····11·······1··1·111·1····1·1···111··················1111111·111··1·1111·111111·····1············1·1··1··········1···11·······1·111·111··1111111·1·1111··1111···········
out 36 (175)	111·1··1·1·1······1·····1·1·1···1······11····1··1·1··1··11·1·1··1····1····1··1·1··1··1···11·1·11···1·1·····1·11···1···1111···1·1·11111·1·1·11····1···1111·11··1·1···1···1····11··1·1··1···11·11·1···1··1·1···1·11·11···11····1·1··111···1·1···11·······1·········1·1·1····1·······11····111···1··11··1··1···1··1···1·1·1·1····1····11·111···1·1······1·1·1··1··1111···1··1·1·1111·1·1·11·······11·1·1··11··1·1··1··1·11··1··1··1···11·11·1····1·1·1····1·11··11···1·1·11····
out 37 (47)	·1····11··········1·············1·····1··················1·····1··········1·········1·1··1····················1·······11···········1···············1·····1···················1·····1··········1··········1··1···1··················1·····11············1··················1······1················1·······1········1········1··1···1·····················1·····11·············1······················1···············1······1··········1··········1··1····1·················
out 38 (143)	1·1·1···11········1····1·········1111··11·1···1···········11·11·11··111··11··1111·1···········1···············1·1111·11111··1······1·········1·······1·111·11·111··1············11·11·11··111··111··1·111··········1··············1·1···1····11········1········1··········1·11·1·11·1··············11··11··11111·11·11111·············1·················11111111111··········1·········1·······1·1·11··11·111·1········11··11·11··111··111···1111············1·············
out 39 (191)	·1··1·11········111·····1111111·····1·111·1·····1·11111··1··1·1111·······11··111····11·1·1111·11···11111111···1··111·1··11····1111··1·······11··1······11··111········1·1····1···11·1·11·····11111·11····1·1·111···11··············1····111·1········111·········1111111········1111·1···111·111··1····1·11·11····11·111····1·1·1··111111···11111111·····1·1111··11·····1111···1·······11·····1···1·1···111······1·1·1···11··1·11·····11111··11···1·1··111····11············
out 40 (167)	1·1·1····1··1·1·1·1·1··11·111·1·111·1·1·1····1··1·1··1··1·1···11·1··1········1·1··1·1·11···1··1····1·1·····1·1····11··1·11····1·1·····1··1·1111·11··········11·1····1···1·····1·1··11··1·1·1·1··1···1··1·11···1·1····1·11····1·1··1·1··11·····1·11···1·1···1····11·111·1··11·1··11·1····111···1··1··1····11··11······1·1·1··1··11····1·1····1·1······1·1····11·1·11·····1·1······1··1·111···1·11·········11·1···1··1··1·1···11··1·1·1·1··1····1·1·11····1·1·····1·1·1·11····
out 41 (143)	1·1·1·1·11·11·1·1·1·1··1···1·····1········1·······························1··1111·1··1·1··111·1···············1·1111·1·111··1111111·1111·····11·····1········1·····························111·111··1·11111·11111·1·11············1·1···11···11111···1·1···1····1···1······1·········1·····························1·11111····1·1···1111·················111111·1111··1·1111·1·1111·····1···1·············1·························111·111···111111·1·1111··1·11···········
out 42 (183)	11··1·11····1····11·····1··11·11·1·1··11··1··1····1·11··1·1··1··1···1·1··1···11·1·1··11···11···1··1·11·11··11·1·11···11111··11·11·····11·11··1··11·····1····1···1··1··1······1···1··1··1·111·111···11···1·1·111····1···11····1·1··11····111·····1·····11·········1··11·1·1·1··1··11··1··1·1··11··1··1···1···1·1·1·1··11·11····11····11··1·11·11·11···11··111··111111··1··11······11·11··1·····11··1······1···1·1·1···1···1···1··1·111·111····11··1·1·1·11·····1···1·1·11····
out 43 (31)	·1···············1·····1···················1·············1·····1················1····1························1···················1··········1················1··············1·····1···············1·······1·······················1··················1·········1·································1·······1·············1·····1··························1···················1··········1··················1·········1······1················1······1·······················
out 44 (175)	111····111······11·····11111111··111··1·1·1·····1·11111···11·1·1··1·111···1·······1·1··1·1111······11111111·····1······1·1··1·1111·11·······1···1····1···11···111·····1·1·······1111··1···1111········1111···111··················111·····1··11······11·········11111111···1·11··1·1·1···111·111····11··1·1···111··1·····1··1···1··1111·····11111111······1·····1·11····1111··11·······1······1·1····1·1···111···1·1····111·1··1···1111········1111····111··················
out 45 (159)	1·1·1···11·······11········1·····1111··11·1··············111·11·11··111··11··1111·1··1········11··············1·1111·11111··1··1··11··········1······1·111·11·111············1··11·11·11··111··111··1·111··1·······11·············1·1···1····11····1··11············1······1·11·1·11·1············1·11··11··11111·11·11111····1········11················11111111111·····1···11·············1···1·1·11··11·111·······1··11··11·11··111··111···1111··1·········11············
out 46 (167)	·1·····11··1·····11·····1·111···111·1········1··1·1··1··1·1·1111·1··1····1····1·1···11····1·1······1·1·····1·1··11·1·1······11·1·1·111·1·1·11·1··1·······11·11·1····1···1·····1·11111··1·1··1111·1····1·1······1··1·1··11····1·1···1······1··1·1······11·········1·111····11·1··1·······111···1··1··1··1111··11···1···1·1···1·1··1··1·1·····1·1······1·1··11·11····1··1··1·1··111·1·1·11····1··1·····1·1·11·1···1··1··1·111·11··1·1··1111·1····1·1·······1···1·1··1·1·11····
out 47 (47)	·················1·····1······1·······1···1··················1·1··········1·····1·····1··1········································1·1········1··1········1···1····················11··········1····1········1···1·····································1·1·······1······1·········1···1··················1·1········1····1······1···1·········································1·1········1·····1······1····1···············1·1··········1·····1·······1····1·················
out 48 (183)	·1··1··1········1·11····111·11······1·11········1·11111··1··1·1111·······11··111····11·1·1111·11···11111111···1··111·11·1·····11111·11······111········11·111·········1·1····1···11·1·11·····11111·11····1·1·111···11··············1····1·1··········1·1·········111·11·········111······111·111··1····1·11·11····11·111····1·1·1··111111···11111111·····1·11111·1······1111·1·11······11···1·····1·1··111·······1·1·1···11··1·11·····11111··11···1·1··111····11············
out 49 (175)	·1·····11··1·····11·····1·1·1·1·111·1···1·1··1··1·1··11·111··11··1··1····1····1·1····1···11·1·1····1·1·····1·1··11·1·1······11·1·1·111·1·1·11···11·······1··1··1····1···1····11·1·1·1··1·1··1111·1····1·11···1·11·111··11····1·1···1······1··1·1······11·········1·1·1·1··11·1··1··1·1··111···11·11·1···11···11···1···1·1·····1····11·11····1·1······1·1··11·11····1··1··1·1··111·1·1·11······11·····1···1··1···1··1111·1·1··1··1·1··1111·1····1·11····1·11··111··1·1·11····
out 50 (167)	······1·1··1······1·····1·1·1···111·1·1·1·1··1··1·1··1··1·1··111·1··1····11···1·1···111···1·1··1···1·1·····1·11·11·1·111····11·1·11111·1·1·11····1··········1··1····1·········1·1·111··1·1··11·1·1····1·1···11·1··1····11····1·1·········1···1·1·······1·········1·1·1····11·1··11·1·1··111·1·1··1··1···111··11···11··1·1···1·11····1·1·1···1·1······1·1·111·1111··1··1··1·1·1111·1·1·11·······1·········1··1···1·····1·1·1·11··1·1··11·1·1····1·1···1·1·1···1····1·1·11····
out 51 (183)	111···1··1·1····11·······1···1··1··11·1···1··1·····11·1·1··1·111·1···11·······1·1·1···11·1·1···1····1·111111·11··1·1·111·1···11·1·11·1·1·1·1·11··1···1····1··11·1···1·1·······1··1111··1·111·1·1·1·····1·1·11·1···1····11····1·1··111····1····11·····11···········1···1···1···1·11··11··1··1·1·1·1···1··111··1·11·····1·11·····11··1·1··1····1·11111·1·1·1·1·1111·1···1·1·1··11·1·1·1·1·1···1··11······1··11·1··11····1··11·11··1·111·1·1·1·····1·1·11··1····1····1·1·11····
out 52 (175)	·······11··1·····1······1·111·1·111·1·1······1··1·1··1··111··11111··1·1··11···1·1···111···1·1··1···1·1·····1·11·11·1·1······11·1·1··11·1·1·11·1·11········1·11·1····1···1····11·1·111··1····11·1·1····1·1···11·1··1····11····1·1··········1··1·1······1··········1·111·1··11·1··11······111···1··11·1···111·111·1·11··1·1···1·11····1·1·1···1·1······1·1·111·11····1··1··1·1···11·1·1·11····1·11·······1·11·1···1··1·11·1·1·111·1····11·1·1····1·1···1·1·1···1····1·1·11····
out 53 (183)	·1··1··1····1·1··11·1···111·11···111··1···1·····1·11111··11111·1····11···11··111····1····1····1····11111111···1··111·11·1····1····11·111····111······1···1····111·····1·1····1··1·11·····11··11111·11·····111···1·1·11·············1····1·1·····11····11···1·····111·11····1·11··1···1···111·111··1·11·11·1···11··11·111····1······1···1····11111111·····1·11111·1··1·1······11·111····11···1···1····1·····111···1·1·1··1·1·1·····11··11111··11····111····1··1·11···········
out 54 (175)	1·1····1·1······11······111·111··111··1·1·1·····1·11111···11·1······111···1·······1·11·1·1111··1···11111111···1·1······1·11·1·1111·11·······111·1····1···11···111·····1·1·······111·······1111········1111·1·111····1·············1·1·····1···1······11··········111·111···1·11··1·1·1···111·111····11··1·····111··1·····1··1·1·1··1111·1···11111111·····11·····1·11····1111··11·······11···1·1·1····1·1···111···1·1····111········1111········1111·1··111·····1············
out 55 (183)	·1··1·1·1··1····1········1·1·11·111···111·1··1·····11·1·111·11··1···1·1···1··1·11···1·11···1········1·111111·1··1·1·····1···111·1··1·1·1·1·111··11·····11111···1····1·1······11·11·1··1·····1···1··11·1·1··11·1·1·1·1··11····1·1···1····11···1·1·····1·········1··1·1·11··11·1···111·1··1··1·1·1·11·1··11···1·1·1··1·1·11···1··11····1·······1·11111·1·1··1·1····1·1··1·1·1···1·1·1·1·111·····11··1·11·11···1···11···11·11··1··1·····1···1···111·1··11··1·1··1·1··1·1·11····
out 56 (183)	······111···1·1·11··1··11·111·1·1··1··111·1··1··1·1··1··1··1·1·11····1····1···1·1···1111···1··1····1·1·····1·11·11·1·11·····1·1·1·11··1··1·1111·11···1·11111·11·1···1···1·····1··1····1···1·1··1·1····1·11·1··1·1····1·11····1·1·········11··1··11···11····1····11·111·1··1···1··111·1··111···1··1···1··1·1·1··1···1··1·1···11111····1·1····1·1······1·1·111·111···1····1·1··11··1··1·111···1·111·1·11·11·11·1··1··1··1··1·····1···1·1··1·1····1·11·1···1·1·····1·1·1·11····
out 57 (55)	·1····1·······1··1·····1······1·······1···1··················1·1·········11·········1·1·······················1·······1···········1··········1··1········1···1····················11·········11··········1··1······················1·····1·······1····1·········1······1·········1···1··················1·1·······11········1··1·························1·····1·······1·····1··········1·····1······1····1···············1·1·········11··········1··1······················
out 58 (183)	11··1··1···11·1··11·1···111·111··111··1·········1·11111···1111·1····111···1··111····11···1····1····11111111···1··111·11·1····1····11·111····111·1····1···1···1111·····1·1·······1·11······1···1111·11·····1·1···1·1·11············11····1·1····111····11···1·····111·111···1·11··1·······111·111····11·11·1···111··1·111····1·1····1···1····11111111····11·11111·1····1······11·111····11···1·1·1····1····1111···1·1····1·1·1······1···1111··11····1·1····1··1·11···········
out 59 (175)	·1··1··1········111·····111·11····1·1··1········1·11111··1····1·11·······11··111····11·1··111··1···11111111···1··111·11·1·····1111··1·······111········111111·········1·1····1····111·11·····11111·11····1·1·1111···1··············1····1·1··········111·········111·11······1··1·1······111·111··1······1··11····11·111····1·1·1···111·1···11111111·····1·11111·1······1111···1·······11···1····11·11·111·······1·1·1····1·11·11·····11111··11···1·1··1111····1············
out 60 (167)	·1··1······11·1··11·1····11·11···111··1·········1·11111···111··1····11····1··111····1·········1····11111111···1··111·1111····1····11·111····111······1···1···1111·····1·1·······1··1·····11···1111·11·····111·····1·11·············1····1······111····11···1······11·11····1·11··1·······111·111····11·1··1···11···1·111····1··········1····11111111·····1·1111111····1······11·111····111··1···1····1····1111···1·1····1···1·····11···1111··11····111·······1·11···········
out 61 (183)	1·1·1····1·1·····1·····11·111···1··1··111····1··1·1··1··11·1·1·11····11····1·1·1··1·1·1··11·1·1····1·1·····1·1····1···1·11···1·1·1··11·1·1·1111··1···1·11111··1·1···1···1····11··1····1··111·1·11···1··1···111·11·111··11····1·1··1·1···1·····11······1·········11·111····1···1··111····111···1··11··1··1·1·1··11····1·1·1··1··1···11·11····1·1······1·1····1··1·11···1··1·1···11·1·1·111···1··11·1·11·11··1·1··1··1·11··1·····1··111·1·11····1·1···11·1·11··111··1·1·11····
out 62 (175)	1·····1·····1···1········111·111·1·11···1····1··1··1··1·111··11··1··1·1···1····11·1·1·11····1·····11·111·11·1···1·11···1·1··111··1··1·11·11·1·1·11······1··1·1··1··1····1········111··1··111····11······11111··11··11··1···1···1··1······1······1····1············111·11·1·1··1·1··1····11·1···1·11·1···11···11·1··1···111··1··11·····1···1·1·111·11··1···1·11··1·11··1·1··1···1·11·11·1····1·11····1···1·1··1·1···1·····11·1··1··111····11······11111···11···11··1··1·1··1·
out 63 (167)	····1···11·11·1·11······11·1···11111··11········1·11···11·111···11·······1···1····1······1111··1···11111·1·1·1···111·····1··11·····11·······111·11···1···1111·········1······11·1·····11·····1·111····1111111·······1········1·111······1····11111···11··········11·1····111·11··11······111····11··11·1····11····1··1···1·········1111·1···11111·1··1·1···111····11··1·······11·······11···1·111····1·111·······1···11·1······11·····1·111····1111111·········1······11·1··
out 64 (175)	·11···1111·1··1·1···1···1···1·11·1·1··111·1··1····1·11··111··1··1···1·····1····1·····111····1·11··1·1··111·111····11··········1··1··11···11··11·11·····1··1·1···1··1··1··········1··1··1··1·111·11·1··11·1·1···11·1111·1···1·1·····11····11··111·1···1·····1·····1···1·1·1·1··1··111·1··1·1··11··11·1···1···1·1····1···1······111·····111·1··1··111··111····11··········1··1···11···11··1···1·11··1····1·1···1·1·1·······1···1··1··1·111·11··1·11·1·1····11··1111·1··11····1
out 65 (175)	111·1····1·1··········1·1·111·1·1··1···1··1··1··1·1··1··1··1·1··1····11··11··1·1··1······11·1·11···1·1·····1·11···1···1·11···1·1·11·11·1·1··1·1·11···1·11··1·11·1···1···1·····1··1·1··1··111··1·1···1··1·1·1·1·11·11···11····1·1··111···1·····11·················1·111·1··1···1···1··1··111···1··1···1··1···1··11·11·1·1·1·········11·111···1·1······1·1·1··1··1·11···1··1·1·1·11·1·1··1····1·111·1·1···1·11·1··1··1··1··1··1··1··111··1·1····1·1·1·1··1·11··11···1·1·11····
out 66 (183)	·1··1···········11······1111111·····1··11·1·····1·11111·······1·11····1··1···111····1111··111··1···11111111···1··111·1111·····1111·11·····1·11··1······111·111········1·1·········111·11·1···1·111·11····1·111111···1··············1····1············11·······1··1111111········1·11·1···111·111·········1··11··1·1··111····1·111···111·1···11111111·····1·1111111······1111··11·····1·11·····1···1·11··111······1·1······1·11·11·1···1·111··11···1·11·1111····1············
out 67 (175)	·1····1·1··1············1·1·1·1·111·1···1·1··1··1·1··1··1·1·1111·1··1····11·1·1·1···111···1·1······1·1·····1·1··11·1·111····11·1·11·11·1·1·11···11·······1··1··1····1···1·····1·11111··1·1··11·111····1·1···11·1··1·1··11····1·1···1·····1···1·1·················1·1·1·1··11·1··1··1·1··111···1··1··1··1111··11···11··1·1···1·11····1·1·····1·1······1·1··11·1111··1··1··1·1·1·11·1·1·11······11·····1···1··1···1··1··1·111·11··1·1··11·111····1·1···1·1·1···1·1··1·1·11····
out 68 (175)	·1·····11···1·1·1·1·1··11·111·1·1··1···11····1··1·11·1··11·1····1····1···1····1·1····1·1·1·1··1····1·1·····1·1··11·1·1······1·1·1·····1··1·1111·11···1·11·11··1·1···1··11····11··111··1···1·1111·1····1·1·111·1······1·11····1·1···1······1··1··11···1·1···1····11·111·1··1···1···11····1111··1··11··1······1··1··1···1·1·····1·1··1·1·1····1·1······1·1··11·11····1····1·1······1··1·111···1·111·1·1··11··1·1··1··1·11··11·1··1···1·1111·1····1·1·111··1·······1·1·1·11····
out 69 (175)	1·1·1·11·1··1·1·11··1··11·1·1·1·111·1·1······1··1·1··1··111···11·1··1·1··1···1·1··1·1111···1··1····1·1·····1·1····1····111····1···11··1··1·111··11········1·11·1····1···1····11·1··11··1···1····1···1··1·111··1·1····1·11····1·1··1·1···111···1·11··111····1····11·1·1·1··11·1··11······111···1··11·1····11··11·1·1··1·1·1··1·111····1·1····1·1······1·1····1···111·····1····11··1··1·111·····11·······1·11·1···1··1·11·1···11··1···1····1····1·1·111···1·1·····1·1·1·11····
out 70 (167)	·1·····11··1·····11·····1·111···111·1········1··1·1··1··1·1··11··1·11·1··1····1·1····1···11·1·1····1·1·····1·1··11·1·1······11·1·1·111·1·1·11·1··1·······11·11·1····1···1·····1·1·1·1·······1111·1····1·11···1·11·111··11····1·1···1······1··1·1······11·········1·111····11·1··1·······111···1··1··1···11···11·1·1···1·1·····1····11·11····1·1······1·1··11·11····1··1··1·1··111·1·1·11····1··1·····1·1·11·1···1··1··1·1·1··1·······1111·1····1·11····1·11··111··1·1·11····
out 71 (47)	·1···············1············1·······1···1·1············1·····1··········1·········1·1··1····················1···················1·············1········1···1··1············1·····1··········1··········1··1···1··················1··················1················1·········1···1············1·······1········1········1··1···1·····················1···················1················1······1····1··1·······1······1··········1··········1··1····1·················
out 72 (167)	111····111·11·1·····1···111111······1·11··1·····1·11111····1111111····1·········1·1·11········11···11111111·····1······1·1··11·······111····11·········11·1111········1·1······1·1··1·11·1·1111····1··111·1·1·····1··1············111·····1··11111·········1·····111111·········111··1···111·111·····1·1111·11··1·······11··1·1········11···11111111······1·····1·11··1·········111····11·········1·1··1111······1·1·····1···1·11·1·1111·····1·111·1·1·······1··1···········
out 73 (159)	·····1·11···1·1·1·1·1···1·111···1··1···11····1··1·1··1··1··1····1····1···11···1······1·1·1·1··1····1·1·····1·11·11·1········1·1·1·····1··1·11·1··1···1·11·11··1·1···1···1·····1··111··1···1·11·1·1·1··1·1·111·1······1·11····1·1··········1··1··11···1·1···1·····1·111····1···1···11····111···1··1···1······1··1··11··1·······1·1··1·1·1····1·1······1·1·111·1·····1····1·1······1··1·11····1··11·1·1··11··1·1··1··1··1··11·1··1···1·11·1·1··1·1·1·111··1·······1·1·1·11····
out 74 (183)	1······111··1·······1··1·1··1···11·11·111····1··1··111·1··1··11·1····11··11···1·1·····11··11······11·111·····1··1·11·1·11····11··111·1···11·111·1·······111·1·11···1··········1··111···1···1·1··11·11·11··111··1··1··1·1···1·1111·1·······1··11·1··········1····1·1··1····11··1·1111····11·1·11·1···1···11··1··11·11··1·1······11···11····1·1·111······1··1·111·11····1·1··1·11·1···11·11···1·1·····11·1·1·11··1······1··11·1···1···1·1··11··1111··111···1···1··1·1··111·1··
out 75 (175)	111····111······11·····1111·11···111··1·········1·111·1··111·1·1····11···1········1·1111·1111······11111111·····1······1·1··1·1111·11·······1·1······1···1···1111·····1·1·1··1··1111·····1111·1·······1111·11111··················111·····1··11······11·········1111·11····1·11··1·······111·1·1··1·11··1·1···11··1······1··1·111··1111·····11111111······1·····1·11····1111··11·······1····1···1····1····1111···1·1·1··111·1·····1111·1·······1111·11·111··················
out 76 (55)	·······1·········11····1······1·······1···1··················1·1·········1······1····1···1·····························11·········11·········1··1········1···1····················11·········1·····1·······1····1·························11··········11········1······1·········1···1··················1·1·······1·····1·····1····1····························11···········11·········1·····1······1····1···············1·1·········1······1······1·····1·················
out 77 (167)	········1···1·1·1·1·1···1·111·111··1···11····1··1·1··1··1··1·1·11····1···11···1·····1··1·1·1··1····1·1·····1·11·11·1·1·1····1·1·1·····1··1·11·1·111··1·11·11··1·1···1···1·····1··1····1···1·11·1·1·1··1·111·1·1······1·11····1·1·············1··11···1·1···1·····1·111·1·11···1···11····111···1··1···1··1·1·1··1··11··1·····1···1··1·1·1····1·1······1·1·111·11·1··1····1·1······1··1·11····1·111·1·1··11··1·1··1··1··1··1·····1···1·11·1·1··1·1·111·1··1·······1·1·1·11····
out 78 (31)	·1··········1·················1···········1··············1············1···1···········1·······················1·································1············1···············1···········1····1·············1······················1············1······················1·············1············1·············1··1···········1·························1···········1························1···········1··········1············1····1·············1······················
out 79 (183)	·1·····111·11·1···1·······1111·111111···1·1·········111111111·1···········1···11··1··111·1····11·····1·11·11111······11·11··111111·1············11···1·1111··1··········1·····1·1·111·········1····11·11111··1111··11·1····1···11··1······1··11111·····1···········1111··111·11·1··1·1·······111111·11·1·1·········1··11·1····111··1···111····1·11·1·111·1····11·111··1·1111··1···············111·1·11·1··1········1··1·1·1·11·········1·····1111111···1111···11·1···1·1·1··
out 80 (175)	·1····111···1·1·111·1··11·111···1··1···11·1··1··1·1··1··11·1····1····1········1·1······1·1·1··1····1·1·····1·1··11·1·11·····1·1·1·1···1··1·1111··1···1·11·11·11·1···1···1····11··1111·1···1·1·11·1····1·1·1·1·1······1·11····1·1···1·····11··1··11···111···1····11·111····1···1···11·1··111···1··11··1·····11··1······1·1·······1··1·1·1····1·1······1·1··11·111···1····1·1··1···1··1·111···1··11·1·1··11·11·1··1··1·11··11·11·1···1·1·11·1····1·1·1·1··1·······1·1·1·11····
out 81 (175)	1·1···1111······1·······111111···111··1·········1·11111···11·1······111··1········1·1·11·1111··1···11111111···1·1·····11·1··1·1111111·1·····11·······1···1···1111·····1·1·······111·······111·1·······1111··1111····1·············1·1····11··11······1···1·······111111····1·11··1·······111·111····11··1·····111·1······1··1··11··1111·1···11111111·····11····11·11····1111·111·1·····11·······1····1····1111···1·1····111········111·1·······1111··1·111·····1············
out 82 (151)	1·1·1···11·11·1·111·11·1······1·········1················1············1··11··1111·1····1··111·1···············1·1111·11111··111111··11111····1··1·········1··················1···········1·11··111··1·11111111111·1·11············1·1···1····11111···111···11···1······1···········1··············1·············1·11·11111······1···1111·················11111111111··1·1111···1111·····1·····1········1·············1············1·11··111···11111111·1111··1·11···········
out 83 (175)	·1··1···1··1····1········1···11·111···111·1··1·····11·1·111··1··1···1·····1··1·11···1··1···1···1····1·111111·1··111···1·1···111·1··1·1·1·1·1·11·11·····11111···1····1·1······11·1··1··1··1··1···1··11·1·1··1··1·1·1····11····1·1···1·1··1····1·1·····1············1···11··11·1···111·1··1··1·1·1·11·1···1···1·1····1·1·11···1···1····1··1····1·11111·1·1··111··1·1·1··1·1·1···1·1·1·1·1·1···1·11··1·11·11···1···11···11·1···1··1··1··1···1···111·1··1···1·1··1····1·1·11····
out 84 (31)	·1·····1······························1···1······1·······1····························1··1····················1········1·································1···1········1······1······························1···1··················1······1······································1···1············1····························1···1·····················1······1····································1····1······1···1·······························1····1·················
out 85 (167)	1·····1··1····1·11······1111··1··1··1·····1·······111··11·11··11······1··1············1···1···1···1···1·1111··1··11···111···11··11···11···11·····1···1·1···111·11··11···1·········11··11··1111·11··11··11··1··111·1·····1··1·1·11·1······1····1··1···11··········1111··1···1····1····1····11·1··11··11···11·····1·1············1····1··1··1····1·111·1···1·11··111·1··1···11····11···11········11·1·····111·11·11··1······1·1··11··1111·11···11·11··1···111··1······111111··
out 86 (31)	·······1··········1···········1···········1·····1············1···········1···········1·································1···········1············1············1·······1············1··········1·············1······························1············1···············1·············1···1··············1·········1···········1·································1·············1···············1···········1···············1···········1·············1·······················
out 87 (31)	······1··········1············1···········1·······1············1··········1···········1·······························1···········1·············1············1·····················1··········1·············1····························1············1················1·············1····1···············1········1···········1·······························1·············1················1···········1·······1·········1··········1·············1······················
out 88 (31)	······1··········1·····1············1····················1············1··1···········1································1···········1··········1·······························1···········1···1·············1·····························1············1·········1···············1·················1·············1·1···········1································1·············1··········1··········1·················1············1···1·············1·······················
out 89 (31)	·······1··········1········1············1················1············1·······················1························1···········1··········1···········1··················1···········1············1············1······················1············1············1··············1··············1·············1·········1············1························1·············1·············1··········1·············1············1············1··············1·············
out 90 (167)	····1··1········1·1·····111·111·····1·11········1·11111·······1111·······1···111····11·1·1111·1····11111111······111·11·1·····11111·1·······111·1····1·11·111·········1·1·········1·1·11·····1·111·11····1·1·111···1····················1·1··········1·1·········111·111····1···111······111·111·········11·11····1··111····1·1·1··11111····11111111·······11111·1······1111·1·1·······11···1·1·1·1·1··111·······1·1······1··1·11·····1·111··11···1·1··111····1·············
out 91 (31)	·1················1···········1·······1··················1····1···········1··············1····················1····················1············1········1···················1················1·················1··················1···················1···············1·········1················1······1·········1···············1·····················1····················1···············1······1···············1·····1···········1··················1·················
out 92 (175)	1·····1··1····1·11······1111··1··1··1·····1·······111··11·11··11······1··1··········1·····1····1··1·111111·1··1··11···111···11··11···11···11·····1···1·1···111·11··11···1·········11··11··1111·11··11··111·11·111·111···1·1····11·1······1····1··1···11··········1111··1···1····1····1····11·1··11··11···11·····1·1·········1·······1···1·1··111111··1···1·11··111·1··1···11····11···11········11·1·····111·11·11··1······1·1··11··1111·11···11·111·11··111··111····1··1·1··
out 93 (159)	111····111·11·1·····1···111·111·····1·111·······1·11111·······1·11····1···········1·11···1·····1···11111111·····1······1·1··11·······111····111·1······11··11·········1·1·········111·11·1·1111·······11··1·1···1·11·1············111·····1··11111·········1·····111·111········1111·····111·111·········1··11··1········1·11·1····1····1···11111111······1·····1·11··1·········111····11···1·1···1·1···11·······1·1······1·11·11·1·1111·······11··1·1····1··11·1···········
out 94 (175)	····1···1··1····1········1·1·1··111···111·1··1·····11·1·111·11·11···1·····1··1·11···1··1···11·······1·111111·11·1·1···1·1···111·1··1·1·1·1·1·1···1·····11111···1····1·1······11·11····1··1··1···1··11·1·1··1··1·1·1·1··11····1·1········1····1·1·····1············1·1·1···11·1···111·1··1··1·1·1·11·1··11·1·1·1····1·1·11···1···1····11······1·11111·1·1·11·1··1·1·1··1·1·1···1·1·1·1·1·1······1··1·11·11···1···11···11·11·····1··1··1···1···111·1··1···1·1·11·1··1·1·11····
out 95 (175)	·1··1···1··1····11·······1·1·11·111···111·1··1·····11·1·1·1·11··1···1········1·11···1··1···1········1·111111·1··1·1···1·1···111·1·11·1·1·1·1·1··11······1111···1····1·1·······1·11·1··1··1··1·1·1··11·1·1··1··1·1·1·1··11····1·1···1····1····1·1·····11···········1·1·11··11·1·1·111·1··1··1·1·1·1··1··11···1·1······1·11···1···1····1·······1·11111·1·1··1·1··1·1·1··1·1·1··11·1·1·1·1·1·····11····11·11···1···11····1·11··1··1··1··1·1·1···111·1··1···1·1··1·1··1·1·11····
out 96 (175)	111······1·1····1······1·1···1··1··11···1·1··1·····11·1·11·1·111·1···1···1····1·1·1·1·11·1·1·1······1·111111·11··1·1·1·1·1···11·1··1·1·1·1·1··1··1···1···1··111·1···1·1······11··1111··1··11···1·1·····1···11·1·····1··11····1·1··111·········11·····1··········1·1···1···1···1·1··1·1··1··1·1·1·11··1··111··1·1··1···1·11··1··11··1·1·······1·11111·1·1·1·1·11·1·1···1·1·1···1·1·1·1·1·····1··11····1···111·1··11···11··11·11··1··11···1·1·····1···11··1······1··1·1·11····
out 97 (159)	······111···1·1··11·1···1·111···1··1···11····1··1·1··1··1··1····1····1········1·······11·1·1··1····1·1·····1·11·11·1·11·····1·1·1·1···1··1·11·1··1···1·11·11··1·1···1···1·····1··111··1···1·1·11·1·1··1·1·1···1······1·11····1·1·········11··1··11····11···1·····1·111····1···1···11····111···1··1···1······1··1······1········11··1·1·1····1·1······1·1·111·111···1····1·1·11···1··1·11····1··11·1·1··11··1·1··1··1··1··11·1··1···1·1·11·1··1·1·1·1····1·······1·1·1·11····
out 98 (175)	········1···1·1·1·1·1··11·111·1·1··1··111·1··1··1·1··1··1··1·1·11····1··111···1·1···1·11···1··1····1·1·····1·11·11·1·1·1····1·1·1·····1··1·1111·11···1·11111·11·1···1···1·····1··1····1···1··1·1·1····1·111···1·1····1·11····1·1·············1··11···1·1···1····11·111·1··1···1··111·1··111···1··1···1··1·1·1··1··11··1·1···1··11····1·1····1·1······1·1·111·11·1··1····1·1······1··1·111···1·111·1·11·11·11·1··1··1··1··1·····1···1··1·1·1····1·111····1·1·····1·1·1·11····
out 99 (175)	·1··1···1··1····1·1······1·1·11·111····11·1··1·····11·1·1·1·11··1···111······1·11·····11···1········1·111111·1··1·1···1·1···111·1····1·1·1·1·1··11·····11·11···1····1·1·······1·11·1··1·····1·1·1··11·1·11·11·1·1·1·1··11····1·1···1····1····1·1·····1·1··········1·1·11··11·1····11·1··1··1·1·1·1··1··11···1·111····1·11······11····1·······1·11111·1·1··1·1··1·1·1··1·1·1·····1·1·1·1·1·····11··1·1··11···1···11····1·11··1··1·1···1·1·1···111·11·11··1·1··1·1··1·1·11····
out 100 (183)	·1··1·111··1····1·1······1··111·111····11·1··1·····11·1·1·1·11··1···1········1·11·····11···1··11····1·111111·1··1·1····11···111·1····1·1·1·1·11111·····11·11···1····1·1·······1·11·1··1··1··1·1·1··11·1·11·11·1·1·11···11····1·1···1····111··1·1·····1·1··········1··111··11·1····11·1··1··1·1·1·1··1··11···1·1······1·11······11····1·11····1·11111·1·1··1·1···11·1··1·1·1·····1·1·1·1·1···1·11··1·1··11···1···11····1·11··1··1··1··1·1·1···111·11·11··1·1··11···1·1·11····
out 101 (167)	1·1····1·1··1·1··1··1····1·1·1··111···111·1··1·····1··1·1·1····11···1····1····1·1·1··1····1·1··1····1·111111·1···1·1·1···1·····1·1··1·1··1·1·1···1·····11111···1····1·1··1····1·1·1···1··1·1···1·1·····1··1111·1···111·11····1·1··1·1·····1···1·11····1····1······1·1·1···11·1···111·1··1··1···1·1··1·····1·1·1···1···1·11····1·····1·1·1····1·11111·1·1···1·11···1······1·1···1·1··1·1·1······1··1·11·11···1···11····1·1·1····1··1·1···1·1·····1··111·1·1····111·1·1·11····
out 102 (47)	·1···············1·····1······1···········1··············1·····1·········11·····1·····1·······················1···················1··········1··11···········1···············1·····1·········11····1········1······················1··················1·········1······11············1············1·······1·······11····1······1·························1···················1··········1·····11··········1··········1······1·········11·····1·······1······················
out 103 (55)	······1··········1············1···········1··············1···1·1····1····11·····1···1·1··1····························1···········1·············1············1···············1····11····1····11····1·····1··1···1························1············1················1·············1············1·····1·1···1···11····1···1··1···1···························1·············1················1···········1··········1····1·1·········11·····1····1··1····1·················
out 104 (31)	······1··········1·········1············1······1············1·············1···········1·······························1···········1···········1···········1·········1············1············1·············1····························1············1·············1··············1···················1···········1···········1·······························1·············1··············1··········1········1········1·············1·············1······················
out 105 (31)	······11·········11·······················································1·········1·1·······························11··········11·······················································1··1··········1··1····························11···········11·························································1·1········1··1·······························11············11·····················································1··1··········1··1······················
out 106 (183)	·1··1·111··1····11·······1·1·11·111····11·1··1·····11·1··11·11··1···1········1·11·····11···1········1·111111·1··1·1····11···111·1·11·1·1·1·1·1··11·····11·11···1····1·1·····111·11·1··1··1··1·1·1··11·1·11·11·1·1·1·1··11····1·1···1····111··1·1·····11···········1·1·11··11·1····11·1··1··1·1·1··1·1··11···1·1······1·11······11····1·······1·11111·1·1··1·1···11·1··1·1·1··11·1·1·1·1·1·····11··1·1··11···1···11···11·11··1··1··1··1·1·1···111·11·11··1·1··1·1··1·1·11····
out 107 (175)	·1··1··1········111·····1111111·····1·11········1·11111··1····1·11·······1···111····11·1·1111·11···11111111···1··111·11·1·····1111··1·······11··1······11·111·········1·1····1····111·11·····1·11··11····1·1·111···11··············1····1·1··········111·········1111111········111······111·111··1······1··11····1·1111····1·1·1··111111···11111111·····1·11111·1······1111···1·······11·····1···1·1··111·······1·1·1····1·11·11·····1·11···11···1·1··111····11············
out 108 (191)	1·1·1·11·1·1······1····11·1·1·1·1··1··11··1··1··1·1··1··11·1·1·11····11··1···1·1··1·1111·11·1·1····1·1·····1·1····1····111···1·1·11111·1·1·111··11···1·111·1·11·1···1···1····11··1····1··111····1···1··1····11·11·111··11····1·1··1·1···111···11·······1········11·1·1·1··1···1··11··1··111···1··11··1··1·1·1··11·1··1·1·1··1·111··11·11····1·1······1·1····1···111···1··1·1·1111·1·1·111·····111·1·11··1·11·1··1··1·11··1·····1··111····1····1·1····111·11··111··1·1·11····
out 109 (47)	·······1··········1···········1···········1············1·····1·1······1·········1···11···1·····························1···········1············1············1·············1······11·····1·········1·····1·1····1·························1············1···············1·············1··········1·······1·1·····1·······1···1·1····1····························1·············1···············1···········1···············1·1·····1··········1····1·1·····1·················
out 110 (183)	·1··1··1········111·····111·11······1·111·1·····1·11111··1····1·11·······11··111····111111111·11···11111111···1··111·11·1·····1111··1·······111········11··111········1·1····1····111·11·····11111·11····1·111·1···11··············1····1·1··········111·········111·11·········1111·1···111·111··1······1··11····11·111····1·111··111111···11111111·····1·11111·1······1111···1·······11···1·····1·1···111······1·1·1····1·11·11·····11111··11···1·11·1·1····11············
out 111 (175)	·1··1··1···11·1···1·1··1111·111··111··1···1·····1·11111··11111······11·1·1···1111···1····1····1····11111111···1··111·11·1····1·····1·111····1·1·1····1···1····111·····1·1····1··1·1······1···1·111··1·····111···1·1·11·············1····1·1····111·····1···1····1111·111···1·11··1···1···111·111··1·11·11·····11··1··1111···1······1···1····11111111·····1·11111·1····1·······1·111····1····1·1·1····1·····111···1·1·1··1·1·······1···1·111···1····111····1··1·11···········
out 112 (175)	·1··1···1··1·1··111······1·1·11·111···111····1·····11·1·1·1·11·11···1·1······1·11······1·1·1········1·111111·1··1·1···1·1···1·1·1·1··1·1·1·1·1··11·····11111·1·1····1·1·······1·11····1·····1·1·1··11·1·11·1··1···1·1··11····1·1···1····1····1·1·····111··········1·1·11··11·1···111····1··1·1·1·1··1··11·1·1·1·1····1·11·······1··1·1·······1·11111·1·1··1·1··1·1·1····1·1··1··1·1·1·1·1·····11··1·11·11·1·1···11····1·11·····1·····1·1·1···111·11·1···1····1·1··1·1·11····
out 113 (175)	11··1·1·1·····1·111·1··1··1···1111······1·1·····1···1····111···1····11·······1··1·1·11·1·11···11·1111···11··11·····1··1111···111···1···1··111·1·1····1··11111·1····11·1·1·····1·····1·11···11····1··1·1··1··11·····1·1·11····1·1··11····11···1···1···111···1····1··1···1·111·······1·1···1···1····1·11····1···11·····1··11··1·1·1··11··11·1·11···11···11·····1·1111···1·11····1···1··111····1·1·1···11·111·1···111·1··1······1·11···11····1···11··1··1·1······1·1·1·1·11····
out 114 (167)	111···1111·11·1··1··1···1111111·····1·11········1·11111··1····1·11·······11·······1·1·1··1·····11··11111111·····1·····11·1··11····1··111····11··1······11·111·········1·1····1····111·11···11·········111·11····1·11··············111····11··11111····1····1·····1111111········111······111·111··1······1··11····11·····1··1··1···1····1···11111111······1····11·11··1······1··111····11·····1···1·1··111·······1·1·1····1·11·11···11·········111·11·····1··11·············
out 115 (47)	······1··········1············1···········1··············1············1··11·····1····11····1··························1···········1·············1············1···············1···········1···11····1·······11····1·······················1············1················1·············1············1·············1·11····1·····11·····1·························1·············1················1···········1··········1············1···11·····1······11······················
check 116 (176)	111·····11·11·1···1·11·1···1···11111··1···1·····1·11111··1····1·11·······1···1111·····11·1111··1···11111111·····1········1··11·····1·111·111·11·11···1···1····111·····1·1····1····111·11·····1·111··1·······1111····1·············111········11111·····1···11···1···1····111·11··1···1···111·111··1······1··11····1··1111······11··1111·1···11111111······1·······11··1·······1·111·111·1···1·111····1·····111···1·1·1····1·11·11·····1·111···1······1·111·····1············
check 117 (168)	····1··1········11······111·111·····1··11·1··1·········11111·1·1····11···11·····1·1·1····1····11···11111111······111·11·1·····1111·11·······111·1······111·111···1·11·········1·1111·····1111······1··111·111···1·1··1··················1·1··········11··········111·111········1·11·1··1·······111·11··1·1···11··11····11··1······1···11···11111111·······11111·1······1111··11·······11···1·1···1·11··111···111·····1·111·1·····1111·······1·111·111····1··1··1···········
check 118 (176)	1·1·1·1·11·11·1·1·1·1······1··1·········1·1··································111··1····1·1111··1··111·1·1111111·1111·1·111··1111111·1111······1·1·········1··1·····························1111111·11·1111111111··11·1111··1·1··1·1·1···11···11111···1·1···1········1··1···········1·1·······························111·1······1··1111·1·1·11·1·111·111·111111·1111··1·1111·1·1111·········1·1········1··1·························1111111··111111111·111···11·111·111··1··
check 119 (232)	1·111···11111111111·1··1······11·1·1·11·11··111·1··1····1····1···11·1··1··1·1111······11·1111··1·1·1·11··1··1·1··111·11111····111···1111·····1··1·1·1·1·1111····1·11·1·1····1·····1··11·1·1111·1·1·111111111·111··11·1·1·1·11··1·1··1·11111·1111·11···111111·1111·11··111·······11···1······1··1··1·1··1111······1··111·11·1·111··1·11·1··1···1·1·11·1··1111··1··1·1·11··1111···1···11·11·11·111···1·1····1········111·1·1111········11111··1·111·1···111·1·11·11··1·1111·1·
check 120 (216)	1·111··11·1····1·1··1·1111·····1·11···111··111·1111·1··1··1·1···1··1···11·1·1·1111····11········11·1····1··1111·····111·1·1·1·111·1··111···11···11·1·11··1·11·1·1·1·1··1·1··11111····11···11·1··1···········1111··111··1··111·1·1·111·1··111····11·1····11···1···1··1·1·1111111·1·1·1····111···111·111···1·111·1·····11·1·11·1··111·1·11···111·1···1··1···1·1·1······1·11·11···11·111··11·1·111····1···11········1··11··11·1·1·111··1111···11·11·1·1····1··111·11···11··1111
check 121 (232)	1111··1··111·1111·1·1·111·····1·1·11111··1··1111··111···1··1··11·111·111·1···11·1111·1111··11···1·1·111111·1··11·1··111·11·1·11····111···111··111111·11··11···111···1·11··1··1··1······1··11·111···1···111·1··11111····1····11···111···11111···1····11··1·1···1·1·1··111·1······1···1·1·1····111·111·111·1·1·1·1···11·1··1·1····1·1·····1··1·1··11·1·111·111·1111·11···11·11····1·111····11·111111··1··111·1···1·11·1·1··1··11·1··1·1···1·11··1···1··1····1·11·11·1111111··1
check 122 (232)	·1··1···1·11···11·111···1····11·111·1111···111···1111·1·111·1·111···11·1·1·11··11··11·1·1··1·1··1···1·1·1·1·····11·11·1·111111·1·····11··1·11·1···11····1··1········1111···11···11·11·1·1···111·11·111·····111111·11···111111···11·1·111····1·11··1111·1·11····11·1···1·11·1·1·1··1··11·11···1·11··11··11··11···1·1·11·111111··1111··1·11···1·1··1·11111··1·1··1·1····1·1·11······111·1·111·1·11··11·1··1·1111··1·1··11·1111···1·111·1111··1·11111··111···1····11·1·1·····11
check 123 (224)	·11··111··1·1······1····1·······1·1·1····11111····1····1·1·1·11···1111·1··1···11·111·····11··1111·1·1····1·1······11·1····1111·11·11·111·11··111·111·1··1·1··1·11··1··1··1111···1·11·1·1111·111·1111111···11·11·111··1·1···1··1··1·11······1111·1····1111111·····1·1111111···1··1·111·1·1·1·1111·1·1·1··11··11··1··1····1·11·········11···1··1··11·11·11····11·1111···1··11·1··1···111··1··1·11·1···1·1·11·1···1·1·1111·1·1·1·11·1···111·11·1···11·11··11··11·11··1··1111111
check 124 (224)	111·1·11·1·1·1·1··11···11·1·1···11···111111111··1·1··1··1·······111111·1·11··1·1··1··1··111111·11··1·1·····1·11···1····111·····1··111··1·1·111···1··1111·11··1······1···1·····11·111·1·11··1··1·1···1··1·1···11111···1·11····1·1··111···111···1·1111111·1111····11·1·1····1·11111···1·1·111···1··1··11111111····1·11·1·1·1··11·1111····1····1·1······1·1·1··1···111·11111·111···11·11·111······1·1·11·1·11·111··1··1··111··1·111·1111··1·1····1·1··1111····11111··1·1·11····
check 125 (224)	·1······1··1·····1···1111·1····1··1111··11·111··1·1··1··111·1111·1··1·1·1·111···1111··1·111111111··1·1·····1·1··11·1·1·1····11·1·1··11·111··11·1·1111·1·11·111111···1···1····11·11111··1········111·111111·1111111·1·1·11····1·1···1·········1·1······1······111··1·11111·111··1·11·111·111···1··11·1··1111··11·111·1111··11111·111·········1·1······1·1··11·11·1··1··1··1·1···11·1··11··111111·1111··11········1··1·11·111·11··1···11111··111·····1··1····111·1··1·1·11····
check 126 (224)	1·1···11·1·1····11·····1·1·1·1··1··11·1·······1111···111····111···11111111·11···11·111111····1111···1·111111·1···1·1·11··1···11·1·11·1·1·1·1·····1···1····1·1·1·1·11·1·1·1111·11··1·111·11·11···111·11······1···11·1·1·11····1·1··1·1····11···11·····11·········1·1·1·1···1···1·11·····11·1111···111111···1111···1·11111·111·1···111111······1·11111·1·1···1·111··1···1·1·1··11·1·1·1·1········11······1·1·1·11·111111·111·11·1·11·1··111··111·111111·1111·111·1··1·1·11····
check 127 (176)	·1·········11·1·111·1··1·········1111·111················1111·1·11··111·········1···1111··111····1·11·1·1···1·1··············11111··1111·····1·······1·11··111111············1··1·111·11··1········1······1··1111·1111·1·11·1·1··1·1···········111···111···1····1··········1·11·1111··············1·11·1·1··11111·······1···1·111···111··111··1·1·1111·1·1············1·1111···1111·····1·······1·1·1···111111·······1··1·1·11·11··1·········1·····1···1111··11111·111111111

The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.

Figures of merit

inputs n460Noisy T states per run.

outputs k116

distance d3Exact, proved and witnessed here.

error coefficient A_{3}3,395Faults of weight 3 in the circuit shown that pass every check and damage the output. The output error is A_{3}\,p^{3} to leading order.

wires N128

checks r12

V_{\mathrm{ex}}116T states per run. CCZ counts as two.

\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.2540Overhead per extractable T state. Lower is better.

\gamma = \log(n/k)/\log d1.2540Overhead per output qubit.

\gamma_T = \log(n/T)/\log dnot computedOverhead per unit of T-count.

T-countnot computedMinimal T-count of the output gate. Not computable at this width.

phase-polynomial degreenot computedMinimised over changes of output basis.

effective width116Rank of the output rows modulo the check rows.

Output gate

116 T0 CS0 CCZon 116 output wires

As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}\cdot \mathrm{T}_{71}\cdot \mathrm{T}_{72}\cdot \mathrm{T}_{73}\cdot \mathrm{T}_{74}\cdot \mathrm{T}_{75}\cdot \mathrm{T}_{76}\cdot \mathrm{T}_{77}\cdot \mathrm{T}_{78}\cdot \mathrm{T}_{79}\cdot \mathrm{T}_{80}\cdot \mathrm{T}_{81}\cdot \mathrm{T}_{82}\cdot \mathrm{T}_{83}\cdot \mathrm{T}_{84}\cdot \mathrm{T}_{85}\cdot \mathrm{T}_{86}\cdot \mathrm{T}_{87}\cdot \mathrm{T}_{88}\cdot \mathrm{T}_{89}\cdot \mathrm{T}_{90}\cdot \mathrm{T}_{91}\cdot \mathrm{T}_{92}\cdot \mathrm{T}_{93}\cdot \mathrm{T}_{94}\cdot \mathrm{T}_{95}\cdot \mathrm{T}_{96}\cdot \mathrm{T}_{97}\cdot \mathrm{T}_{98}\cdot \mathrm{T}_{99}\cdot \mathrm{T}_{100}\cdot \mathrm{T}_{101}\cdot \mathrm{T}_{102}\cdot \mathrm{T}_{103}\cdot \mathrm{T}_{104}\cdot \mathrm{T}_{105}\cdot \mathrm{T}_{106}\cdot \mathrm{T}_{107}\cdot \mathrm{T}_{108}\cdot \mathrm{T}_{109}\cdot \mathrm{T}_{110}\cdot \mathrm{T}_{111}\cdot \mathrm{T}_{112}\cdot \mathrm{T}_{113}\cdot \mathrm{T}_{114}\cdot \mathrm{T}_{115}

As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100+101+102+103+104+105+106+107+108+109+110+111+112+113+114+115 (output wires per term, separated by +)

This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.

Clifford correction

With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 116 single-wire gates: \mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{S} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{S} on output 23 and 92 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

All 116 correction gates

\mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{S} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{S} on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25, \mathrm{S} on output 26, \mathrm{S} on output 27, \mathrm{S} on output 28, \mathrm{S} on output 29, \mathrm{S} on output 30, \mathrm{S} on output 31, \mathrm{S} on output 32, \mathrm{S} on output 33, \mathrm{S} on output 34, \mathrm{S} on output 35, \mathrm{S} on output 36, \mathrm{S} on output 37, \mathrm{S} on output 38, \mathrm{S} on output 39, \mathrm{S} on output 40, \mathrm{S} on output 41, \mathrm{S} on output 42, \mathrm{S} on output 43, \mathrm{S} on output 44, \mathrm{S} on output 45, \mathrm{S} on output 46, \mathrm{S} on output 47, \mathrm{S} on output 48, \mathrm{S} on output 49, \mathrm{S} on output 50, \mathrm{S} on output 51, \mathrm{S} on output 52, \mathrm{S} on output 53, \mathrm{S} on output 54, \mathrm{S} on output 55, \mathrm{S} on output 56, \mathrm{S} on output 57, \mathrm{S} on output 58, \mathrm{S} on output 59, \mathrm{S} on output 60, \mathrm{S} on output 61, \mathrm{S} on output 62, \mathrm{S} on output 63, \mathrm{S} on output 64, \mathrm{S} on output 65, \mathrm{S} on output 66, \mathrm{S} on output 67, \mathrm{S} on output 68, \mathrm{S} on output 69, \mathrm{S} on output 70, \mathrm{S} on output 71, \mathrm{S} on output 72, \mathrm{S} on output 73, \mathrm{S} on output 74, \mathrm{S} on output 75, \mathrm{S} on output 76, \mathrm{S} on output 77, \mathrm{S} on output 78, \mathrm{S} on output 79, \mathrm{S} on output 80, \mathrm{S} on output 81, \mathrm{S} on output 82, \mathrm{S} on output 83, \mathrm{S} on output 84, \mathrm{S} on output 85, \mathrm{S} on output 86, \mathrm{S} on output 87, \mathrm{S} on output 88, \mathrm{S} on output 89, \mathrm{S} on output 90, \mathrm{S} on output 91, \mathrm{S} on output 92, \mathrm{S} on output 93, \mathrm{S} on output 94, \mathrm{S} on output 95, \mathrm{S} on output 96, \mathrm{S} on output 97, \mathrm{S} on output 98, \mathrm{S} on output 99, \mathrm{S} on output 100, \mathrm{S} on output 101, \mathrm{S} on output 102, \mathrm{S} on output 103, \mathrm{S} on output 104, \mathrm{S} on output 105, \mathrm{S} on output 106, \mathrm{S} on output 107, \mathrm{S} on output 108, \mathrm{S} on output 109, \mathrm{S} on output 110, \mathrm{S} on output 111, \mathrm{S} on output 112, \mathrm{S} on output 113, \mathrm{S} on output 114, \mathrm{S} on output 115

Or no Clifford gate at all: run every rotation as \mathrm{T}^\dagger. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.

Rotations are numbered by matrix column, from 0. The correction comes from the columns by the weight expansion of Bravyi and Haah (2012). verify_catalog.py re-derives it, checks the corrected circuit's phase input by input against the gate, and on small circuits simulates it gate by gate.

Convert the output with CNOT and S

A CNOT circuit on the outputs, followed by S, Z and CZ gates, turns this factory's gate into other gates that prepare the same magic state. Type a target gate to check whether it is reachable. If it is, you get the circuit, checked on every basis state.

Or list every gate it reaches. The list is built in your browser and saved as a text file, one gate per line.

Python code that writes the same list

import json, urllib.request

NAMES = {1: "T", 2: "CS", 3: "CCZ"}


def equivalent_gates(k, terms, limit=1_000_000):
    """Every gate a CNOT circuit and S, Z, CZ gates reach from this one.

    A gate is its set of terms mod Clifford: {a} is T, {a,b} is CS and
    {a,b,c} is CCZ on those outputs. CNOT c->t sends x_t to
    x_c + x_t - 2 x_c x_t, so a term on t but not c adds the term with t
    replaced by c, and, below CCZ, the term with c added.
    """
    start = frozenset(frozenset(m) for m in terms)
    seen, queue = {start}, [start]
    for gate in queue:
        for c in range(k):
            for t in range(k):
                if c == t:
                    continue
                new = set(gate)
                for m in gate:
                    if t in m and c not in m:
                        new ^= {(m - {t}) | {c}}
                        if len(m) < 3:
                            new ^= {m | {c}}
                new = frozenset(new)
                if new not in seen:
                    seen.add(new)
                    queue.append(new)
                    if len(seen) > limit:
                        raise RuntimeError(f"more than {limit} equivalent gates")
    return seen


def name(gate, k):
    sep = "," if k > 10 else ""
    terms = sorted((sorted(m) for m in gate), key=lambda m: (len(m), m))
    return "·".join(NAMES[len(m)] + sep.join(map(str, m)) for m in terms) or "I"


url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/460.116.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-460.116.3.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.

Exactly 3,395 faults of weight 3 are undetectable and damaging, so A_{3}=3{,}395. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{3}\,p^{3}+O(p^{4}).

A damaging fault of weight 3 sits on columns [0,2,5].

A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.

Original source

S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535

Provenance

built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows

Found by: AI search (gamma frontier): from Wills parent codes

Discovery: AI search

1 recorded source

[
 {
  "regime": "AI search (gamma frontier): from Wills parent codes",
  "file": "gamma_frontier_release/protocols/restricted_light_460_116_3.json",
  "label": "restricted_light_460_116_3",
  "N": 128,
  "d": 3,
  "d_is_exact": true,
  "origin": "Wills-derived restricted-light construction",
  "provenance": "gamma frontier release record restricted_light_460_116_3 (source catalogue id restricted_light_460_116_3); construction: Wills-derived restricted-light construction; matrix 8d088005ae3d3724...; the release states d=3 (exact), gamma=1.2539785988075356 (exact)",
  "notes": "matrix gamma_frontier_release/matrices/8d088005ae3d372403cc6f00b15e325c674c1645534e4cec50a1891fe05a717a.matrix"
 }
]

Use it in code

Load this factory and re-derive every number from its circuit with the catalogue's own verifier.

# git clone https://github.com/shubhamj810/magic-state-factory-repo
# cd magic-state-factory-repo/master_catalog
import json, urllib.request
import verify_catalog as VC

url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/460.116.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]

facts, problems = VC.derive(columns, k, N)    # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N)  # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
      problems or "verified")

Raw record

Show the JSON this page is built from

Source: master_catalog.json, factories[1066].