{"id":"575.1.6.a","row":1149,"stored":{"file":"master_catalog.json","row":1149,"construction":null,"columns_sha256":null},"parameters":{"n":575,"k":1,"d":6,"N":148,"r":147,"level":3},"gate":{"string":"0","human":"T0","monomials":[[0]],"sk_key":[[0]],"sk_fingerprint":"bc179efd84e614ba","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,5,6,12,14,15,17,19,20,21,22,25,26,27,28,30,31,32,36,37],[0,2,3,4,6,7,13,15,16,18,20,21,22,23,26,27,28,29,31,32,33,37,38],[0,3,4,5,7,8,14,16,17,19,21,22,23,24,27,28,29,30,32,33,34,38,39],[0,1,2,3,4,8,9,12,14,18,19,21,23,24,26,27,29,32,33,34,35,36,37,39],[0,1,4,6,9,10,12,13,14,17,21,24,26,31,32,33,34,35,38],[0,2,5,7,10,11,13,14,15,18,22,25,27,32,33,34,35,36,39],[0,1,2,5,8,11,16,17,20,21,22,23,25,27,30,31,32,33,34,35],[0,2,3,6,9,12,17,18,21,22,23,24,26,28,31,32,33,34,35,36],[0,3,4,7,10,13,18,19,22,23,24,25,27,29,32,33,34,35,36,37],[0,4,5,8,11,14,19,20,23,24,25,26,28,30,33,34,35,36,37,38],[0,5,6,9,12,15,20,21,24,25,26,27,29,31,34,35,36,37,38,39],[0,1,2,3,5,7,10,12,13,14,15,16,17,19,20,31,35,38,39],[0,1,4,5,8,11,12,13,16,18,19,22,25,26,27,28,30,31,37,39],[0,1,3,9,13,15,21,22,23,25,29,30,36,37,38],[0,2,4,10,14,16,22,23,24,26,30,31,37,38,39],[0,1,2,6,11,12,14,19,20,21,22,23,24,26,28,30,36,37,38,39],[0,1,5,6,7,13,14,17,19,23,24,26,28,29,30,32,36,38,39],[0,1,3,5,7,8,12,17,18,19,21,22,24,26,28,29,32,33,36,39],[0,1,3,4,5,8,9,12,13,14,15,17,18,21,23,26,28,29,31,32,33,34,36],[0,2,4,5,6,9,10,13,14,15,16,18,19,22,24,27,29,30,32,33,34,35,37],[0,3,5,6,7,10,11,14,15,16,17,19,20,23,25,28,30,31,33,34,35,36,38],[0,4,6,7,8,11,12,15,16,17,18,20,21,24,26,29,31,32,34,35,36,37,39],[0,1,2,3,6,7,8,9,13,14,15,16,18,20,26,28,31,33,35,38],[0,2,3,4,7,8,9,10,14,15,16,17,19,21,27,29,32,34,36,39],[0,1,2,4,6,8,9,10,11,12,14,16,18,19,21,25,26,27,31,32,33,35,36],[0,2,3,5,7,9,10,11,12,13,15,17,19,20,22,26,27,28,32,33,34,36,37],[0,3,4,6,8,10,11,12,13,14,16,18,20,21,23,27,28,29,33,34,35,37,38],[0,4,5,7,9,11,12,13,14,15,17,19,21,22,24,28,29,30,34,35,36,38,39],[0,1,2,3,8,10,13,16,17,18,19,21,23,26,27,28,29,32,35,39],[0,1,4,5,6,9,11,12,15,18,21,24,25,26,29,31,32,33,37],[0,2,5,6,7,10,12,13,16,19,22,25,26,27,30,32,33,34,38],[0,3,6,7,8,11,13,14,17,20,23,26,27,28,31,33,34,35,39],[0,1,2,3,4,5,6,7,8,9,17,18,19,20,22,24,25,26,29,30,31,34,35,37],[0,2,3,4,5,6,7,8,9,10,18,19,20,21,23,25,26,27,30,31,32,35,36,38],[0,3,4,5,6,7,8,9,10,11,19,20,21,22,24,26,27,28,31,32,33,36,37,39],[0,1,2,3,4,7,8,9,10,11,14,15,17,19,23,26,29,30,31,33,34,36,38],[0,2,3,4,5,8,9,10,11,12,15,16,18,20,24,27,30,31,32,34,35,37,39],[0,1,2,4,9,10,11,13,14,15,16,20,22,26,27,30,33,35,37,38],[0,2,3,5,10,11,12,14,15,16,17,21,23,27,28,31,34,36,38,39],[0,1,2,4,5,11,13,14,16,18,19,20,21,24,25,26,27,29,30,31,35,36,39],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[0,11],[0,12],[0,13],[0,14],[0,15],[0,16],[0,17],[0,18],[0,19],[0,20],[0,21],[0,22],[0,23],[0,24],[0,25],[0,26],[0,27],[0,28],[0,29],[0,30],[0,31],[0,32],[0,33],[0,34],[0,35],[0,36],[0,37],[0,38],[0,39],[0,1,2,3,5,6,12,14,15,17,19,20,21,22,25,26,27,28,30,31,32,36,37,147],[0,2,3,4,6,7,13,15,16,18,20,21,22,23,26,27,28,29,31,32,33,37,38,147],[0,3,4,5,7,8,14,16,17,19,21,22,23,24,27,28,29,30,32,33,34,38,39,147],[0,1,2,3,4,8,9,12,14,18,19,21,23,24,26,27,29,32,33,34,35,36,37,39,147],[0,1,4,6,9,10,12,13,14,17,21,24,26,31,32,33,34,35,38,147],[0,2,5,7,10,11,13,14,15,18,22,25,27,32,33,34,35,36,39,147],[0,1,2,5,8,11,16,17,20,21,22,23,25,27,30,31,32,33,34,35,147],[0,2,3,6,9,12,17,18,21,22,23,24,26,28,31,32,33,34,35,36,147],[0,3,4,7,10,13,18,19,22,23,24,25,27,29,32,33,34,35,36,37,147],[0,4,5,8,11,14,19,20,23,24,25,26,28,30,33,34,35,36,37,38,147],[0,5,6,9,12,15,20,21,24,25,26,27,29,31,34,35,36,37,38,39,147],[0,1,2,3,5,7,10,12,13,14,15,16,17,19,20,31,35,38,39,147],[0,1,4,5,8,11,12,13,16,18,19,22,25,26,27,28,30,31,37,39,147],[0,1,3,9,13,15,21,22,23,25,29,30,36,37,38,147],[0,2,4,10,14,16,22,23,24,26,30,31,37,38,39,147],[0,1,2,6,11,12,14,19,20,21,22,23,24,26,28,30,36,37,38,39,147],[0,1,5,6,7,13,14,17,19,23,24,26,28,29,30,32,36,38,39,147],[0,1,3,5,7,8,12,17,18,19,21,22,24,26,28,29,32,33,36,39,147],[0,1,3,4,5,8,9,12,13,14,15,17,18,21,23,26,28,29,31,32,33,34,36,147],[0,2,4,5,6,9,10,13,14,15,16,18,19,22,24,27,29,30,32,33,34,35,37,147],[0,3,5,6,7,10,11,14,15,16,17,19,20,23,25,28,30,31,33,34,35,36,38,147],[0,4,6,7,8,11,12,15,16,17,18,20,21,24,26,29,31,32,34,35,36,37,39,147],[0,1,2,3,6,7,8,9,13,14,15,16,18,20,26,28,31,33,35,38,147],[0,2,3,4,7,8,9,10,14,15,16,17,19,21,27,29,32,34,36,39,147],[0,1,2,4,6,8,9,10,11,12,14,16,18,19,21,25,26,27,31,32,33,35,36,147],[0,2,3,5,7,9,10,11,12,13,15,17,19,20,22,26,27,28,32,33,34,36,37,147],[0,3,4,6,8,10,11,12,13,14,16,18,20,21,23,27,28,29,33,34,35,37,38,147],[0,4,5,7,9,11,12,13,14,15,17,19,21,22,24,28,29,30,34,35,36,38,39,147],[0,1,2,3,8,10,13,16,17,18,19,21,23,26,27,28,29,32,35,39,147],[0,1,4,5,6,9,11,12,15,18,21,24,25,26,29,31,32,33,37,147],[0,2,5,6,7,10,12,13,16,19,22,25,26,27,30,32,33,34,38,147],[0,3,6,7,8,11,13,14,17,20,23,26,27,28,31,33,34,35,39,147],[0,1,2,3,4,5,6,7,8,9,17,18,19,20,22,24,25,26,29,30,31,34,35,37,147],[0,2,3,4,5,6,7,8,9,10,18,19,20,21,23,25,26,27,30,31,32,35,36,38,147],[0,3,4,5,6,7,8,9,10,11,19,20,21,22,24,26,27,28,31,32,33,36,37,39,147],[0,1,2,3,4,7,8,9,10,11,14,15,17,19,23,26,29,30,31,33,34,36,38,147],[0,2,3,4,5,8,9,10,11,12,15,16,18,20,24,27,30,31,32,34,35,37,39,147],[0,1,2,4,9,10,11,13,14,15,16,20,22,26,27,30,33,35,37,38,147],[0,2,3,5,10,11,12,14,15,16,17,21,23,27,28,31,34,36,38,39,147],[0,1,2,4,5,11,13,14,16,18,19,20,21,24,25,26,27,29,30,31,35,36,39,147],[0,1,147],[0,2,147],[0,3,147],[0,4,147],[0,5,147],[0,6,147],[0,7,147],[0,8,147],[0,9,147],[0,10,147],[0,11,147],[0,12,147],[0,13,147],[0,14,147],[0,15,147],[0,16,147],[0,17,147],[0,18,147],[0,19,147],[0,20,147],[0,21,147],[0,22,147],[0,23,147],[0,24,147],[0,25,147],[0,26,147],[0,27,147],[0,28,147],[0,29,147],[0,30,147],[0,31,147],[0,32,147],[0,33,147],[0,34,147],[0,35,147],[0,36,147],[0,37,147],[0,38,147],[0,39,147],[0,44,48,49,54,55,57,58,59,60,61,62,63,67,69,72,73,147],[0,45,49,50,51,55,56,58,59,60,61,62,63,64,68,70,73,147],[0,40,42,44,45,52,54,56,57,60,65,66,68,71,73,147],[0,41,43,45,46,51,53,55,57,58,61,66,67,69,72,147],[0,42,44,46,47,52,54,56,58,59,62,67,68,70,73,147],[0,43,45,47,48,51,53,55,57,59,60,63,68,69,71,147],[0,44,46,48,49,52,54,56,58,60,61,64,69,70,72,147],[0,45,47,49,50,53,55,57,59,61,62,65,70,71,73,147],[0,40,42,44,45,48,56,58,59,60,61,64,68,69,71,72,73,147],[0,41,43,45,46,49,51,57,59,60,61,62,65,69,70,72,73,147],[0,42,44,46,47,50,51,52,58,60,61,62,63,66,70,71,73,147],[0,40,42,43,44,46,47,48,50,52,53,54,66,67,68,69,71,72,73,147],[0,40,41,42,43,46,47,48,49,50,53,55,59,61,62,63,64,66,67,70,72,147],[0,40,41,43,45,46,47,48,49,51,56,59,60,61,65,66,67,69,71,147],[0,41,42,44,46,47,48,49,50,52,57,60,61,62,66,67,68,70,72,147],[0,40,43,44,46,47,48,49,51,53,54,58,59,64,66,67,71,147],[0,41,44,45,47,48,49,50,52,54,55,59,60,65,67,68,72,147],[0,40,44,48,49,51,53,54,55,56,59,60,62,63,64,147],[0,41,45,49,50,52,54,55,56,57,60,61,63,64,65,147],[0,40,44,45,51,53,54,55,56,57,58,59,63,65,68,69,73,147],[0,41,45,46,51,52,54,55,56,57,58,59,60,64,66,69,70,147],[0,42,46,47,52,53,55,56,57,58,59,60,61,65,67,70,71,147],[0,43,47,48,53,54,56,57,58,59,60,61,62,66,68,71,72,147],[0,40,42,44,45,46,50,51,54,59,61,62,63,64,66,68,69,73,147],[0,40,41,42,43,44,47,50,52,54,55,59,60,61,65,66,67,68,70,73,147],[0,40,41,43,46,48,50,53,54,55,56,59,60,63,64,67,71,73,147],[0,40,41,45,46,47,49,50,55,56,57,59,60,62,63,65,66,69,72,73,147],[0,40,41,44,45,47,48,54,56,57,58,59,60,62,67,68,69,70,147],[0,41,42,45,46,48,49,55,57,58,59,60,61,63,68,69,70,71,147],[0,42,43,46,47,49,50,56,58,59,60,61,62,64,69,70,71,72,147],[0,40,42,43,45,46,47,48,51,54,57,60,64,65,66,68,69,70,71,72,147],[0,41,43,44,46,47,48,49,52,55,58,61,65,66,67,69,70,71,72,73,147],[0,42,44,45,47,48,49,50,51,53,56,59,62,66,67,68,70,71,72,73,147],[0,40,42,43,44,48,49,52,57,59,60,61,62,64,66,67,71,72,147],[0,41,43,44,45,49,50,53,58,60,61,62,63,65,67,68,72,73,147],[0,40,147],[0,41,147],[0,42,147],[0,43,147],[0,44,147],[0,45,147],[0,46,147],[0,47,147],[0,48,147],[0,49,147],[0,50,147],[0,51,147],[0,52,147],[0,53,147],[0,54,147],[0,55,147],[0,56,147],[0,57,147],[0,58,147],[0,59,147],[0,60,147],[0,61,147],[0,62,147],[0,63,147],[0,64,147],[0,65,147],[0,66,147],[0,67,147],[0,68,147],[0,69,147],[0,70,147],[0,71,147],[0,72,147],[0,73,147],[0,44,48,49,54,55,57,58,59,60,61,62,63,67,69,72,73,146,147],[0,45,49,50,51,55,56,58,59,60,61,62,63,64,68,70,73,146,147],[0,40,42,44,45,52,54,56,57,60,65,66,68,71,73,146,147],[0,41,43,45,46,51,53,55,57,58,61,66,67,69,72,146,147],[0,42,44,46,47,52,54,56,58,59,62,67,68,70,73,146,147],[0,43,45,47,48,51,53,55,57,59,60,63,68,69,71,146,147],[0,44,46,48,49,52,54,56,58,60,61,64,69,70,72,146,147],[0,45,47,49,50,53,55,57,59,61,62,65,70,71,73,146,147],[0,40,42,44,45,48,56,58,59,60,61,64,68,69,71,72,73,146,147],[0,41,43,45,46,49,51,57,59,60,61,62,65,69,70,72,73,146,147],[0,42,44,46,47,50,51,52,58,60,61,62,63,66,70,71,73,146,147],[0,40,42,43,44,46,47,48,50,52,53,54,66,67,68,69,71,72,73,146,147],[0,40,41,42,43,46,47,48,49,50,53,55,59,61,62,63,64,66,67,70,72,146,147],[0,40,41,43,45,46,47,48,49,51,56,59,60,61,65,66,67,69,71,146,147],[0,41,42,44,46,47,48,49,50,52,57,60,61,62,66,67,68,70,72,146,147],[0,40,43,44,46,47,48,49,51,53,54,58,59,64,66,67,71,146,147],[0,41,44,45,47,48,49,50,52,54,55,59,60,65,67,68,72,146,147],[0,40,44,48,49,51,53,54,55,56,59,60,62,63,64,146,147],[0,41,45,49,50,52,54,55,56,57,60,61,63,64,65,146,147],[0,40,44,45,51,53,54,55,56,57,58,59,63,65,68,69,73,146,147],[0,41,45,46,51,52,54,55,56,57,58,59,60,64,66,69,70,146,147],[0,42,46,47,52,53,55,56,57,58,59,60,61,65,67,70,71,146,147],[0,43,47,48,53,54,56,57,58,59,60,61,62,66,68,71,72,146,147],[0,40,42,44,45,46,50,51,54,59,61,62,63,64,66,68,69,73,146,147],[0,40,41,42,43,44,47,50,52,54,55,59,60,61,65,66,67,68,70,73,146,147],[0,40,41,43,46,48,50,53,54,55,56,59,60,63,64,67,71,73,146,147],[0,40,41,45,46,47,49,50,55,56,57,59,60,62,63,65,66,69,72,73,146,147],[0,40,41,44,45,47,48,54,56,57,58,59,60,62,67,68,69,70,146,147],[0,41,42,45,46,48,49,55,57,58,59,60,61,63,68,69,70,71,146,147],[0,42,43,46,47,49,50,56,58,59,60,61,62,64,69,70,71,72,146,147],[0,40,42,43,45,46,47,48,51,54,57,60,64,65,66,68,69,70,71,72,146,147],[0,41,43,44,46,47,48,49,52,55,58,61,65,66,67,69,70,71,72,73,146,147],[0,42,44,45,47,48,49,50,51,53,56,59,62,66,67,68,70,71,72,73,146,147],[0,40,42,43,44,48,49,52,57,59,60,61,62,64,66,67,71,72,146,147],[0,41,43,44,45,49,50,53,58,60,61,62,63,65,67,68,72,73,146,147],[0,40,146,147],[0,41,146,147],[0,42,146,147],[0,43,146,147],[0,44,146,147],[0,45,146,147],[0,46,146,147],[0,47,146,147],[0,48,146,147],[0,49,146,147],[0,50,146,147],[0,51,146,147],[0,52,146,147],[0,53,146,147],[0,54,146,147],[0,55,146,147],[0,56,146,147],[0,57,146,147],[0,58,146,147],[0,59,146,147],[0,60,146,147],[0,61,146,147],[0,62,146,147],[0,63,146,147],[0,64,146,147],[0,65,146,147],[0,66,146,147],[0,67,146,147],[0,68,146,147],[0,69,146,147],[0,70,146,147],[0,71,146,147],[0,72,146,147],[0,73,146,147],[0,74,75,76,77,79,80,81,83,84,86,87,88,92,93,146,147],[0,75,76,77,78,80,81,82,84,85,87,88,89,93,94,146,147],[0,76,77,78,79,81,82,83,85,86,88,89,90,94,95,146,147],[0,77,78,79,80,82,83,84,86,87,89,90,91,95,96,146,147],[0,74,75,76,77,78,85,86,90,91,93,96,146,147],[0,74,78,80,81,83,84,88,91,93,94,146,147],[0,75,79,81,82,84,85,89,92,94,95,146,147],[0,76,80,82,83,85,86,90,93,95,96,146,147],[0,74,75,76,79,80,88,91,92,93,94,96,146,147],[0,74,79,83,84,86,87,88,89,94,95,146,147],[0,75,80,84,85,87,88,89,90,95,96,146,147],[0,74,75,77,79,80,83,84,85,87,89,90,91,92,93,96,146,147],[0,74,77,78,79,83,85,87,90,91,94,146,147],[0,75,78,79,80,84,86,88,91,92,95,146,147],[0,76,79,80,81,85,87,89,92,93,96,146,147],[0,74,75,76,79,82,83,84,87,90,92,94,146,147],[0,75,76,77,80,83,84,85,88,91,93,95,146,147],[0,76,77,78,81,84,85,86,89,92,94,96,146,147],[0,74,75,76,78,80,81,82,83,84,85,88,90,92,95,146,147],[0,75,76,77,79,81,82,83,84,85,86,89,91,93,96,146,147],[0,74,75,78,79,81,82,85,88,90,93,94,146,147],[0,75,76,79,80,82,83,86,89,91,94,95,146,147],[0,76,77,80,81,83,84,87,90,92,95,96,146,147],[0,74,75,76,78,79,80,82,83,85,86,87,91,92,96,146,147],[0,74,146,147],[0,75,146,147],[0,76,146,147],[0,77,146,147],[0,78,146,147],[0,79,146,147],[0,80,146,147],[0,81,146,147],[0,82,146,147],[0,83,146,147],[0,84,146,147],[0,85,146,147],[0,86,146,147],[0,87,146,147],[0,88,146,147],[0,89,146,147],[0,90,146,147],[0,91,146,147],[0,92,146,147],[0,93,146,147],[0,94,146,147],[0,95,146,147],[0,96,146,147],[0,74,75,76,77,79,80,81,83,84,86,87,88,92,93,145,146,147],[0,75,76,77,78,80,81,82,84,85,87,88,89,93,94,145,146,147],[0,76,77,78,79,81,82,83,85,86,88,89,90,94,95,145,146,147],[0,77,78,79,80,82,83,84,86,87,89,90,91,95,96,145,146,147],[0,74,75,76,77,78,85,86,90,91,93,96,145,146,147],[0,74,78,80,81,83,84,88,91,93,94,145,146,147],[0,75,79,81,82,84,85,89,92,94,95,145,146,147],[0,76,80,82,83,85,86,90,93,95,96,145,146,147],[0,74,75,76,79,80,88,91,92,93,94,96,145,146,147],[0,74,79,83,84,86,87,88,89,94,95,145,146,147],[0,75,80,84,85,87,88,89,90,95,96,145,146,147],[0,74,75,77,79,80,83,84,85,87,89,90,91,92,93,96,145,146,147],[0,74,77,78,79,83,85,87,90,91,94,145,146,147],[0,75,78,79,80,84,86,88,91,92,95,145,146,147],[0,76,79,80,81,85,87,89,92,93,96,145,146,147],[0,74,75,76,79,82,83,84,87,90,92,94,145,146,147],[0,75,76,77,80,83,84,85,88,91,93,95,145,146,147],[0,76,77,78,81,84,85,86,89,92,94,96,145,146,147],[0,74,75,76,78,80,81,82,83,84,85,88,90,92,95,145,146,147],[0,75,76,77,79,81,82,83,84,85,86,89,91,93,96,145,146,147],[0,74,75,78,79,81,82,85,88,90,93,94,145,146,147],[0,75,76,79,80,82,83,86,89,91,94,95,145,146,147],[0,76,77,80,81,83,84,87,90,92,95,96,145,146,147],[0,74,75,76,78,79,80,82,83,85,86,87,91,92,96,145,146,147],[0,74,145,146,147],[0,75,145,146,147],[0,76,145,146,147],[0,77,145,146,147],[0,78,145,146,147],[0,79,145,146,147],[0,80,145,146,147],[0,81,145,146,147],[0,82,145,146,147],[0,83,145,146,147],[0,84,145,146,147],[0,85,145,146,147],[0,86,145,146,147],[0,87,145,146,147],[0,88,145,146,147],[0,89,145,146,147],[0,90,145,146,147],[0,91,145,146,147],[0,92,145,146,147],[0,93,145,146,147],[0,94,145,146,147],[0,95,145,146,147],[0,96,145,146,147],[0,97,98,99,103,110,112,114,117,145,146,147],[0,97,99,102,106,107,109,112,113,114,116,117,118,145,146,147],[0,97,102,103,104,106,108,109,110,111,112,113,116,118,145,146,147],[0,101,102,103,104,106,107,108,110,111,113,114,115,145,146,147],[0,97,98,99,102,104,105,107,108,109,110,111,115,116,117,145,146,147],[0,97,98,100,101,102,111,112,114,115,116,117,118,145,146,147],[0,97,99,100,101,103,104,106,107,109,111,113,114,118,145,146,147],[0,100,104,106,107,109,110,114,117,145,146,147],[0,97,98,99,101,103,105,107,108,111,112,114,115,117,118,145,146,147],[0,97,98,100,101,103,104,105,110,112,113,114,116,118,145,146,147],[0,99,104,108,109,111,112,113,114,145,146,147],[0,97,98,99,100,103,105,109,113,115,117,145,146,147],[0,97,98,100,102,103,104,105,108,109,115,116,118,145,146,147],[0,97,99,100,101,102,103,105,107,110,111,112,114,115,145,146,147],[0,100,103,104,105,109,111,113,116,117,145,146,147],[0,98,99,100,103,106,107,108,111,114,116,118,145,146,147],[0,99,100,101,104,107,108,109,112,115,117,145,146,147],[0,97,102,104,107,109,110,111,113,114,118,145,146,147],[0,97,98,99,101,102,106,109,111,112,145,146,147],[0,99,100,101,103,105,106,107,108,109,110,113,115,117,145,146,147],[0,98,99,102,103,105,106,109,112,114,117,118,145,146,147],[0,99,100,103,104,106,107,110,113,115,118,145,146,147],[0,97,145,146,147],[0,98,99,100,102,103,104,106,107,109,110,111,115,116,145,146,147],[0,98,145,146,147],[0,99,145,146,147],[0,100,145,146,147],[0,101,145,146,147],[0,102,145,146,147],[0,103,145,146,147],[0,104,145,146,147],[0,105,145,146,147],[0,106,145,146,147],[0,107,145,146,147],[0,108,145,146,147],[0,109,145,146,147],[0,110,145,146,147],[0,111,145,146,147],[0,112,145,146,147],[0,113,145,146,147],[0,114,145,146,147],[0,115,145,146,147],[0,116,145,146,147],[0,117,145,146,147],[0,118,145,146,147],[0,97,98,99,103,110,112,114,117,144,145,146,147],[0,97,99,102,106,107,109,112,113,114,116,117,118,144,145,146,147],[0,97,102,103,104,106,108,109,110,111,112,113,116,118,144,145,146,147],[0,101,102,103,104,106,107,108,110,111,113,114,115,144,145,146,147],[0,97,98,99,102,104,105,107,108,109,110,111,115,116,117,144,145,146,147],[0,97,98,100,101,102,111,112,114,115,116,117,118,144,145,146,147],[0,97,99,100,101,103,104,106,107,109,111,113,114,118,144,145,146,147],[0,100,104,106,107,109,110,114,117,144,145,146,147],[0,97,98,99,101,103,105,107,108,111,112,114,115,117,118,144,145,146,147],[0,97,98,100,101,103,104,105,110,112,113,114,116,118,144,145,146,147],[0,99,104,108,109,111,112,113,114,144,145,146,147],[0,97,98,99,100,103,105,109,113,115,117,144,145,146,147],[0,97,98,100,102,103,104,105,108,109,115,116,118,144,145,146,147],[0,97,99,100,101,102,103,105,107,110,111,112,114,115,144,145,146,147],[0,100,103,104,105,109,111,113,116,117,144,145,146,147],[0,98,99,100,103,106,107,108,111,114,116,118,144,145,146,147],[0,99,100,101,104,107,108,109,112,115,117,144,145,146,147],[0,97,102,104,107,109,110,111,113,114,118,144,145,146,147],[0,97,98,99,101,102,106,109,111,112,144,145,146,147],[0,99,100,101,103,105,106,107,108,109,110,113,115,117,144,145,146,147],[0,98,99,102,103,105,106,109,112,114,117,118,144,145,146,147],[0,99,100,103,104,106,107,110,113,115,118,144,145,146,147],[0,97,144,145,146,147],[0,98,99,100,102,103,104,106,107,109,110,111,115,116,144,145,146,147],[0,98,144,145,146,147],[0,99,144,145,146,147],[0,100,144,145,146,147],[0,101,144,145,146,147],[0,102,144,145,146,147],[0,103,144,145,146,147],[0,104,144,145,146,147],[0,105,144,145,146,147],[0,106,144,145,146,147],[0,107,144,145,146,147],[0,108,144,145,146,147],[0,109,144,145,146,147],[0,110,144,145,146,147],[0,111,144,145,146,147],[0,112,144,145,146,147],[0,113,144,145,146,147],[0,114,144,145,146,147],[0,115,144,145,146,147],[0,116,144,145,146,147],[0,117,144,145,146,147],[0,118,144,145,146,147],[0,119,120,124,125,126,128,144,145,146,147],[0,120,121,125,126,127,129,144,145,146,147],[0,119,120,121,122,124,125,127,144,145,146,147],[0,120,121,122,123,125,126,128,144,145,146,147],[0,121,122,123,124,126,127,129,144,145,146,147],[0,119,120,122,123,126,127,144,145,146,147],[0,120,121,123,124,127,128,144,145,146,147],[0,121,122,124,125,128,129,144,145,146,147],[0,119,120,122,123,124,128,129,144,145,146,147],[0,119,121,123,126,128,129,144,145,146,147],[0,119,122,125,126,127,128,129,144,145,146,147],[0,119,123,124,125,127,129,144,145,146,147],[0,119,144,145,146,147],[0,120,144,145,146,147],[0,121,144,145,146,147],[0,122,144,145,146,147],[0,123,144,145,146,147],[0,124,144,145,146,147],[0,125,144,145,146,147],[0,126,144,145,146,147],[0,127,144,145,146,147],[0,128,144,145,146,147],[0,129,144,145,146,147],[0,119,120,124,125,126,128,143,144,145,146,147],[0,120,121,125,126,127,129,143,144,145,146,147],[0,119,120,121,122,124,125,127,143,144,145,146,147],[0,120,121,122,123,125,126,128,143,144,145,146,147],[0,121,122,123,124,126,127,129,143,144,145,146,147],[0,119,120,122,123,126,127,143,144,145,146,147],[0,120,121,123,124,127,128,143,144,145,146,147],[0,121,122,124,125,128,129,143,144,145,146,147],[0,119,120,122,123,124,128,129,143,144,145,146,147],[0,119,121,123,126,128,129,143,144,145,146,147],[0,119,122,125,126,127,128,129,143,144,145,146,147],[0,119,123,124,125,127,129,143,144,145,146,147],[0,119,143,144,145,146,147],[0,120,143,144,145,146,147],[0,121,143,144,145,146,147],[0,122,143,144,145,146,147],[0,123,143,144,145,146,147],[0,124,143,144,145,146,147],[0,125,143,144,145,146,147],[0,126,143,144,145,146,147],[0,127,143,144,145,146,147],[0,128,143,144,145,146,147],[0,129,143,144,145,146,147],[0,131,137,143,144,145,146,147],[0,130,136,137,143,144,145,146,147],[0,130,136,143,144,145,146,147],[0,135,137,143,144,145,146,147],[0,131,132,134,143,144,145,146,147],[0,135,136,143,144,145,146,147],[0,133,137,143,144,145,146,147],[0,130,133,137,143,144,145,146,147],[0,130,133,143,144,145,146,147],[0,132,134,143,144,145,146,147],[0,132,143,144,145,146,147],[0,135,143,144,145,146,147],[0,135,136,137,143,144,145,146,147],[0,131,132,143,144,145,146,147],[0,133,143,144,145,146,147],[0,134,137,143,144,145,146,147],[0,131,134,137,143,144,145,146,147],[0,131,137,142,143,144,145,146,147],[0,130,136,137,142,143,144,145,146,147],[0,130,136,142,143,144,145,146,147],[0,135,137,142,143,144,145,146,147],[0,131,132,134,142,143,144,145,146,147],[0,135,136,142,143,144,145,146,147],[0,133,137,142,143,144,145,146,147],[0,130,133,137,142,143,144,145,146,147],[0,130,133,142,143,144,145,146,147],[0,132,134,142,143,144,145,146,147],[0,132,142,143,144,145,146,147],[0,135,142,143,144,145,146,147],[0,135,136,137,142,143,144,145,146,147],[0,131,132,142,143,144,145,146,147],[0,133,142,143,144,145,146,147],[0,134,137,142,143,144,145,146,147],[0,131,134,137,142,143,144,145,146,147],[0,138,139,142,143,144,145,146,147],[0,139,140,142,143,144,145,146,147],[0,138,139,140,142,143,144,145,146,147],[0,138,140,142,143,144,145,146,147],[0,138,142,143,144,145,146,147],[0,139,142,143,144,145,146,147],[0,140,142,143,144,145,146,147],[0,138,139,141,142,143,144,145,146,147],[0,139,140,141,142,143,144,145,146,147],[0,138,139,140,141,142,143,144,145,146,147],[0,138,140,141,142,143,144,145,146,147],[0,138,141,142,143,144,145,146,147],[0,139,141,142,143,144,145,146,147],[0,140,141,142,143,144,145,146,147],[0,141,142,143,144,145,146,147]]},"distance":{"d":6,"is_exact":false,"upper":15,"witness":[0,79,158,227,296,343,390,435,480,503,526,543,560,567,574],"A_d":null,"certified":{"d":15,"is_exact":false,"met":true,"source":"Jain and Albert (arXiv:2408.12752), Table I: [[79,1,15]] quantum QR code (extended QR [80,40,16]) doubled onto [[417,1,13]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 15, with d_sd at least the classical distance less one (their Lemma 2.4); the [[69,1,13]] input's distance is proved here by enumerating every word of SD70 through the punctured coordinate"}},"clifford":{"kind":"powers","correction":{"S":[[0,1],[51,2],[52,2],[53,2],[54,2],[55,2],[56,2],[57,2],[58,2],[59,2],[60,2],[61,2],[62,2],[63,2],[64,2],[65,2],[66,2],[67,2],[68,2],[69,2],[70,2],[71,2],[72,2],[73,2],[97,2],[100,2],[101,2],[104,2],[105,2],[107,2],[108,2],[111,2],[114,2],[116,2],[144,2],[146,2]],"CZ":[[51,146],[52,146],[53,146],[54,146],[55,146],[56,146],[57,146],[58,146],[59,146],[60,146],[61,146],[62,146],[63,146],[64,146],[65,146],[66,146],[67,146],[68,146],[69,146],[70,146],[71,146],[72,146],[73,146],[97,144],[100,144],[101,144],[104,144],[105,144],[107,144],[108,144],[111,144],[114,144],[116,144]]},"rotation_powers":[[0,7],[1,7],[2,7],[4,7],[5,7],[11,7],[13,7],[14,7],[16,7],[18,7],[19,7],[20,7],[21,7],[24,7],[25,7],[26,7],[27,7],[29,7],[30,7],[31,7],[35,7],[36,7],[39,7],[82,3],[85,3],[86,3],[87,3],[88,3],[89,3],[91,3],[94,3],[96,3],[101,3],[102,3],[107,3],[111,3],[112,3],[113,3],[116,3],[117,3],[119,3],[120,3],[121,3],[122,3],[123,3],[124,3],[125,3],[126,3],[127,3],[128,3],[129,3],[130,3],[131,3],[132,3],[133,3],[134,3],[135,3],[136,3],[137,3],[138,3],[139,3],[140,3],[141,3],[142,3],[143,3],[144,3],[145,3],[146,3],[147,3],[148,3],[149,3],[150,3],[151,3],[152,3],[153,3],[154,3],[155,3],[156,3],[157,3],[160,3],[161,3],[162,3],[163,3],[164,3],[165,3],[169,3],[171,3],[172,3],[175,3],[176,3],[181,3],[183,3],[185,3],[186,3],[187,3],[191,3],[192,3],[229,3],[230,3],[231,3],[232,3],[233,3],[234,3],[238,3],[240,3],[241,3],[244,3],[245,3],[250,3],[252,3],[254,3],[255,3],[256,3],[260,3],[261,3],[391,3],[394,3],[395,3],[401,3],[402,3],[403,3],[404,3],[405,3],[406,3],[408,3],[409,3],[410,3],[413,3],[434,3],[435,3],[437,3],[438,3],[441,3],[442,3],[443,3],[444,3],[445,3],[452,3],[456,3],[457,3],[459,3],[460,3],[461,3],[462,3],[463,3],[464,3],[465,3],[466,3],[467,3],[468,3],[469,3],[470,3],[471,3],[472,3],[473,3],[474,3],[475,3],[476,3],[477,3],[478,3],[480,3],[484,3],[485,3],[486,3],[488,3],[490,3],[502,3],[503,3],[507,3],[508,3],[509,3],[511,3],[513,3],[525,3],[527,3],[528,3],[530,3],[536,3],[542,3],[543,3],[546,3],[548,3],[549,3],[550,3],[551,3],[552,3],[554,3],[555,3],[556,3],[557,3],[558,3]]},"metrics":{"gamma":3.546441444807884,"gamma_t":3.546441444807884,"gamma_rho":3.546441444807884,"gamma_claim":2.3464742412127526,"gamma_t_claim":2.3464742412127526,"gamma_rho_claim":2.3464742412127526,"v_ex":1,"rate":0.0017391304347826088,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Jain-Albert doubling: triorthogonal family"],"discovery":"pre-existing","strongest_claim":"a code of the triorthogonal family of Jain and Albert (arXiv:2408.12752, Table I; transversal_t_codes/), self-dual CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction; a verified witness, not a maximum","sources":[{"regime":"Jain-Albert doubling: triorthogonal family","file":"transversal_t_codes/factories.json","label":"JA-575","N":148,"d":6,"d_is_exact":false,"origin":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance\", IEEE J. Sel. Areas Inf. Theory 6, 127 (2025), arXiv:2408.12752","provenance":"[[79,1,15]] quantum QR code (extended QR [80,40,16]) doubled onto [[417,1,13]] (Table I)","notes":"its [[69,1,13]] input is the self-dual [70,35,12] code found by transversal_t_codes/search_sd70.py, whose words through the punctured coordinate all weigh at least 14, in place of the paper's [70,35,14] code, which is only formally self-dual"}]},"references":[{"key":"jain2025transversal","short":"Jain & Albert (2025)","full":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance,\" IEEE J. Sel. Areas Inf. Theory 6, 127-137 (2025); arXiv:2408.12752.","url":"https://doi.org/10.1109/JSAIT.2025.3570832","date":"2025-05-16"}]}