{"id":"599.1.6.a","row":1153,"stored":{"file":"master_catalog.json","row":1153,"construction":null,"columns_sha256":null},"parameters":{"n":599,"k":1,"d":6,"N":154,"r":153,"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],[0,1,2,3,5,6,12,14,15,17,19,20,21,22,25,26,27,28,30,31,32,36,37,153],[0,2,3,4,6,7,13,15,16,18,20,21,22,23,26,27,28,29,31,32,33,37,38,153],[0,3,4,5,7,8,14,16,17,19,21,22,23,24,27,28,29,30,32,33,34,38,39,153],[0,1,2,3,4,8,9,12,14,18,19,21,23,24,26,27,29,32,33,34,35,36,37,39,153],[0,1,4,6,9,10,12,13,14,17,21,24,26,31,32,33,34,35,38,153],[0,2,5,7,10,11,13,14,15,18,22,25,27,32,33,34,35,36,39,153],[0,1,2,5,8,11,16,17,20,21,22,23,25,27,30,31,32,33,34,35,153],[0,2,3,6,9,12,17,18,21,22,23,24,26,28,31,32,33,34,35,36,153],[0,3,4,7,10,13,18,19,22,23,24,25,27,29,32,33,34,35,36,37,153],[0,4,5,8,11,14,19,20,23,24,25,26,28,30,33,34,35,36,37,38,153],[0,5,6,9,12,15,20,21,24,25,26,27,29,31,34,35,36,37,38,39,153],[0,1,2,3,5,7,10,12,13,14,15,16,17,19,20,31,35,38,39,153],[0,1,4,5,8,11,12,13,16,18,19,22,25,26,27,28,30,31,37,39,153],[0,1,3,9,13,15,21,22,23,25,29,30,36,37,38,153],[0,2,4,10,14,16,22,23,24,26,30,31,37,38,39,153],[0,1,2,6,11,12,14,19,20,21,22,23,24,26,28,30,36,37,38,39,153],[0,1,5,6,7,13,14,17,19,23,24,26,28,29,30,32,36,38,39,153],[0,1,3,5,7,8,12,17,18,19,21,22,24,26,28,29,32,33,36,39,153],[0,1,3,4,5,8,9,12,13,14,15,17,18,21,23,26,28,29,31,32,33,34,36,153],[0,2,4,5,6,9,10,13,14,15,16,18,19,22,24,27,29,30,32,33,34,35,37,153],[0,3,5,6,7,10,11,14,15,16,17,19,20,23,25,28,30,31,33,34,35,36,38,153],[0,4,6,7,8,11,12,15,16,17,18,20,21,24,26,29,31,32,34,35,36,37,39,153],[0,1,2,3,6,7,8,9,13,14,15,16,18,20,26,28,31,33,35,38,153],[0,2,3,4,7,8,9,10,14,15,16,17,19,21,27,29,32,34,36,39,153],[0,1,2,4,6,8,9,10,11,12,14,16,18,19,21,25,26,27,31,32,33,35,36,153],[0,2,3,5,7,9,10,11,12,13,15,17,19,20,22,26,27,28,32,33,34,36,37,153],[0,3,4,6,8,10,11,12,13,14,16,18,20,21,23,27,28,29,33,34,35,37,38,153],[0,4,5,7,9,11,12,13,14,15,17,19,21,22,24,28,29,30,34,35,36,38,39,153],[0,1,2,3,8,10,13,16,17,18,19,21,23,26,27,28,29,32,35,39,153],[0,1,4,5,6,9,11,12,15,18,21,24,25,26,29,31,32,33,37,153],[0,2,5,6,7,10,12,13,16,19,22,25,26,27,30,32,33,34,38,153],[0,3,6,7,8,11,13,14,17,20,23,26,27,28,31,33,34,35,39,153],[0,1,2,3,4,5,6,7,8,9,17,18,19,20,22,24,25,26,29,30,31,34,35,37,153],[0,2,3,4,5,6,7,8,9,10,18,19,20,21,23,25,26,27,30,31,32,35,36,38,153],[0,3,4,5,6,7,8,9,10,11,19,20,21,22,24,26,27,28,31,32,33,36,37,39,153],[0,1,2,3,4,7,8,9,10,11,14,15,17,19,23,26,29,30,31,33,34,36,38,153],[0,2,3,4,5,8,9,10,11,12,15,16,18,20,24,27,30,31,32,34,35,37,39,153],[0,1,2,4,9,10,11,13,14,15,16,20,22,26,27,30,33,35,37,38,153],[0,2,3,5,10,11,12,14,15,16,17,21,23,27,28,31,34,36,38,39,153],[0,1,2,4,5,11,13,14,16,18,19,20,21,24,25,26,27,29,30,31,35,36,39,153],[0,1,153],[0,2,153],[0,3,153],[0,4,153],[0,5,153],[0,6,153],[0,7,153],[0,8,153],[0,9,153],[0,10,153],[0,11,153],[0,12,153],[0,13,153],[0,14,153],[0,15,153],[0,16,153],[0,17,153],[0,18,153],[0,19,153],[0,20,153],[0,21,153],[0,22,153],[0,23,153],[0,24,153],[0,25,153],[0,26,153],[0,27,153],[0,28,153],[0,29,153],[0,30,153],[0,31,153],[0,32,153],[0,33,153],[0,34,153],[0,35,153],[0,36,153],[0,37,153],[0,38,153],[0,39,153],[0,40,41,42,44,45,51,53,54,56,58,59,60,61,64,65,66,67,69,70,71,75,76,153],[0,41,42,43,45,46,52,54,55,57,59,60,61,62,65,66,67,68,70,71,72,76,77,153],[0,42,43,44,46,47,53,55,56,58,60,61,62,63,66,67,68,69,71,72,73,77,78,153],[0,40,41,42,43,47,48,51,53,57,58,60,62,63,65,66,68,71,72,73,74,75,76,78,153],[0,40,43,45,48,49,51,52,53,56,60,63,65,70,71,72,73,74,77,153],[0,41,44,46,49,50,52,53,54,57,61,64,66,71,72,73,74,75,78,153],[0,40,41,44,47,50,55,56,59,60,61,62,64,66,69,70,71,72,73,74,153],[0,41,42,45,48,51,56,57,60,61,62,63,65,67,70,71,72,73,74,75,153],[0,42,43,46,49,52,57,58,61,62,63,64,66,68,71,72,73,74,75,76,153],[0,43,44,47,50,53,58,59,62,63,64,65,67,69,72,73,74,75,76,77,153],[0,44,45,48,51,54,59,60,63,64,65,66,68,70,73,74,75,76,77,78,153],[0,40,41,42,44,46,49,51,52,53,54,55,56,58,59,70,74,77,78,153],[0,40,43,44,47,50,51,52,55,57,58,61,64,65,66,67,69,70,76,78,153],[0,40,42,48,52,54,60,61,62,64,68,69,75,76,77,153],[0,41,43,49,53,55,61,62,63,65,69,70,76,77,78,153],[0,40,41,45,50,51,53,58,59,60,61,62,63,65,67,69,75,76,77,78,153],[0,40,44,45,46,52,53,56,58,62,63,65,67,68,69,71,75,77,78,153],[0,40,42,44,46,47,51,56,57,58,60,61,63,65,67,68,71,72,75,78,153],[0,40,42,43,44,47,48,51,52,53,54,56,57,60,62,65,67,68,70,71,72,73,75,153],[0,41,43,44,45,48,49,52,53,54,55,57,58,61,63,66,68,69,71,72,73,74,76,153],[0,42,44,45,46,49,50,53,54,55,56,58,59,62,64,67,69,70,72,73,74,75,77,153],[0,43,45,46,47,50,51,54,55,56,57,59,60,63,65,68,70,71,73,74,75,76,78,153],[0,40,41,42,45,46,47,48,52,53,54,55,57,59,65,67,70,72,74,77,153],[0,41,42,43,46,47,48,49,53,54,55,56,58,60,66,68,71,73,75,78,153],[0,40,41,43,45,47,48,49,50,51,53,55,57,58,60,64,65,66,70,71,72,74,75,153],[0,41,42,44,46,48,49,50,51,52,54,56,58,59,61,65,66,67,71,72,73,75,76,153],[0,42,43,45,47,49,50,51,52,53,55,57,59,60,62,66,67,68,72,73,74,76,77,153],[0,43,44,46,48,50,51,52,53,54,56,58,60,61,63,67,68,69,73,74,75,77,78,153],[0,40,41,42,47,49,52,55,56,57,58,60,62,65,66,67,68,71,74,78,153],[0,40,43,44,45,48,50,51,54,57,60,63,64,65,68,70,71,72,76,153],[0,41,44,45,46,49,51,52,55,58,61,64,65,66,69,71,72,73,77,153],[0,42,45,46,47,50,52,53,56,59,62,65,66,67,70,72,73,74,78,153],[0,40,41,42,43,44,45,46,47,48,56,57,58,59,61,63,64,65,68,69,70,73,74,76,153],[0,41,42,43,44,45,46,47,48,49,57,58,59,60,62,64,65,66,69,70,71,74,75,77,153],[0,42,43,44,45,46,47,48,49,50,58,59,60,61,63,65,66,67,70,71,72,75,76,78,153],[0,40,41,42,43,46,47,48,49,50,53,54,56,58,62,65,68,69,70,72,73,75,77,153],[0,41,42,43,44,47,48,49,50,51,54,55,57,59,63,66,69,70,71,73,74,76,78,153],[0,40,41,43,48,49,50,52,53,54,55,59,61,65,66,69,72,74,76,77,153],[0,41,42,44,49,50,51,53,54,55,56,60,62,66,67,70,73,75,77,78,153],[0,40,41,43,44,50,52,53,55,57,58,59,60,63,64,65,66,68,69,70,74,75,78,153],[0,40,153],[0,41,153],[0,42,153],[0,43,153],[0,44,153],[0,45,153],[0,46,153],[0,47,153],[0,48,153],[0,49,153],[0,50,153],[0,51,153],[0,52,153],[0,53,153],[0,54,153],[0,55,153],[0,56,153],[0,57,153],[0,58,153],[0,59,153],[0,60,153],[0,61,153],[0,62,153],[0,63,153],[0,64,153],[0,65,153],[0,66,153],[0,67,153],[0,68,153],[0,69,153],[0,70,153],[0,71,153],[0,72,153],[0,73,153],[0,74,153],[0,75,153],[0,76,153],[0,77,153],[0,78,153],[0,40,41,42,44,45,51,53,54,56,58,59,60,61,64,65,66,67,69,70,71,75,76,152,153],[0,41,42,43,45,46,52,54,55,57,59,60,61,62,65,66,67,68,70,71,72,76,77,152,153],[0,42,43,44,46,47,53,55,56,58,60,61,62,63,66,67,68,69,71,72,73,77,78,152,153],[0,40,41,42,43,47,48,51,53,57,58,60,62,63,65,66,68,71,72,73,74,75,76,78,152,153],[0,40,43,45,48,49,51,52,53,56,60,63,65,70,71,72,73,74,77,152,153],[0,41,44,46,49,50,52,53,54,57,61,64,66,71,72,73,74,75,78,152,153],[0,40,41,44,47,50,55,56,59,60,61,62,64,66,69,70,71,72,73,74,152,153],[0,41,42,45,48,51,56,57,60,61,62,63,65,67,70,71,72,73,74,75,152,153],[0,42,43,46,49,52,57,58,61,62,63,64,66,68,71,72,73,74,75,76,152,153],[0,43,44,47,50,53,58,59,62,63,64,65,67,69,72,73,74,75,76,77,152,153],[0,44,45,48,51,54,59,60,63,64,65,66,68,70,73,74,75,76,77,78,152,153],[0,40,41,42,44,46,49,51,52,53,54,55,56,58,59,70,74,77,78,152,153],[0,40,43,44,47,50,51,52,55,57,58,61,64,65,66,67,69,70,76,78,152,153],[0,40,42,48,52,54,60,61,62,64,68,69,75,76,77,152,153],[0,41,43,49,53,55,61,62,63,65,69,70,76,77,78,152,153],[0,40,41,45,50,51,53,58,59,60,61,62,63,65,67,69,75,76,77,78,152,153],[0,40,44,45,46,52,53,56,58,62,63,65,67,68,69,71,75,77,78,152,153],[0,40,42,44,46,47,51,56,57,58,60,61,63,65,67,68,71,72,75,78,152,153],[0,40,42,43,44,47,48,51,52,53,54,56,57,60,62,65,67,68,70,71,72,73,75,152,153],[0,41,43,44,45,48,49,52,53,54,55,57,58,61,63,66,68,69,71,72,73,74,76,152,153],[0,42,44,45,46,49,50,53,54,55,56,58,59,62,64,67,69,70,72,73,74,75,77,152,153],[0,43,45,46,47,50,51,54,55,56,57,59,60,63,65,68,70,71,73,74,75,76,78,152,153],[0,40,41,42,45,46,47,48,52,53,54,55,57,59,65,67,70,72,74,77,152,153],[0,41,42,43,46,47,48,49,53,54,55,56,58,60,66,68,71,73,75,78,152,153],[0,40,41,43,45,47,48,49,50,51,53,55,57,58,60,64,65,66,70,71,72,74,75,152,153],[0,41,42,44,46,48,49,50,51,52,54,56,58,59,61,65,66,67,71,72,73,75,76,152,153],[0,42,43,45,47,49,50,51,52,53,55,57,59,60,62,66,67,68,72,73,74,76,77,152,153],[0,43,44,46,48,50,51,52,53,54,56,58,60,61,63,67,68,69,73,74,75,77,78,152,153],[0,40,41,42,47,49,52,55,56,57,58,60,62,65,66,67,68,71,74,78,152,153],[0,40,43,44,45,48,50,51,54,57,60,63,64,65,68,70,71,72,76,152,153],[0,41,44,45,46,49,51,52,55,58,61,64,65,66,69,71,72,73,77,152,153],[0,42,45,46,47,50,52,53,56,59,62,65,66,67,70,72,73,74,78,152,153],[0,40,41,42,43,44,45,46,47,48,56,57,58,59,61,63,64,65,68,69,70,73,74,76,152,153],[0,41,42,43,44,45,46,47,48,49,57,58,59,60,62,64,65,66,69,70,71,74,75,77,152,153],[0,42,43,44,45,46,47,48,49,50,58,59,60,61,63,65,66,67,70,71,72,75,76,78,152,153],[0,40,41,42,43,46,47,48,49,50,53,54,56,58,62,65,68,69,70,72,73,75,77,152,153],[0,41,42,43,44,47,48,49,50,51,54,55,57,59,63,66,69,70,71,73,74,76,78,152,153],[0,40,41,43,48,49,50,52,53,54,55,59,61,65,66,69,72,74,76,77,152,153],[0,41,42,44,49,50,51,53,54,55,56,60,62,66,67,70,73,75,77,78,152,153],[0,40,41,43,44,50,52,53,55,57,58,59,60,63,64,65,66,68,69,70,74,75,78,152,153],[0,40,152,153],[0,41,152,153],[0,42,152,153],[0,43,152,153],[0,44,152,153],[0,45,152,153],[0,46,152,153],[0,47,152,153],[0,48,152,153],[0,49,152,153],[0,50,152,153],[0,51,152,153],[0,52,152,153],[0,53,152,153],[0,54,152,153],[0,55,152,153],[0,56,152,153],[0,57,152,153],[0,58,152,153],[0,59,152,153],[0,60,152,153],[0,61,152,153],[0,62,152,153],[0,63,152,153],[0,64,152,153],[0,65,152,153],[0,66,152,153],[0,67,152,153],[0,68,152,153],[0,69,152,153],[0,70,152,153],[0,71,152,153],[0,72,152,153],[0,73,152,153],[0,74,152,153],[0,75,152,153],[0,76,152,153],[0,77,152,153],[0,78,152,153],[0,79,80,81,82,84,85,86,88,89,91,92,93,97,98,152,153],[0,80,81,82,83,85,86,87,89,90,92,93,94,98,99,152,153],[0,81,82,83,84,86,87,88,90,91,93,94,95,99,100,152,153],[0,82,83,84,85,87,88,89,91,92,94,95,96,100,101,152,153],[0,79,80,81,82,83,90,91,95,96,98,101,152,153],[0,79,83,85,86,88,89,93,96,98,99,152,153],[0,80,84,86,87,89,90,94,97,99,100,152,153],[0,81,85,87,88,90,91,95,98,100,101,152,153],[0,79,80,81,84,85,93,96,97,98,99,101,152,153],[0,79,84,88,89,91,92,93,94,99,100,152,153],[0,80,85,89,90,92,93,94,95,100,101,152,153],[0,79,80,82,84,85,88,89,90,92,94,95,96,97,98,101,152,153],[0,79,82,83,84,88,90,92,95,96,99,152,153],[0,80,83,84,85,89,91,93,96,97,100,152,153],[0,81,84,85,86,90,92,94,97,98,101,152,153],[0,79,80,81,84,87,88,89,92,95,97,99,152,153],[0,80,81,82,85,88,89,90,93,96,98,100,152,153],[0,81,82,83,86,89,90,91,94,97,99,101,152,153],[0,79,80,81,83,85,86,87,88,89,90,93,95,97,100,152,153],[0,80,81,82,84,86,87,88,89,90,91,94,96,98,101,152,153],[0,79,80,83,84,86,87,90,93,95,98,99,152,153],[0,80,81,84,85,87,88,91,94,96,99,100,152,153],[0,81,82,85,86,88,89,92,95,97,100,101,152,153],[0,79,80,81,83,84,85,87,88,90,91,92,96,97,101,152,153],[0,79,152,153],[0,80,152,153],[0,81,152,153],[0,82,152,153],[0,83,152,153],[0,84,152,153],[0,85,152,153],[0,86,152,153],[0,87,152,153],[0,88,152,153],[0,89,152,153],[0,90,152,153],[0,91,152,153],[0,92,152,153],[0,93,152,153],[0,94,152,153],[0,95,152,153],[0,96,152,153],[0,97,152,153],[0,98,152,153],[0,99,152,153],[0,100,152,153],[0,101,152,153],[0,79,80,81,82,84,85,86,88,89,91,92,93,97,98,151,152,153],[0,80,81,82,83,85,86,87,89,90,92,93,94,98,99,151,152,153],[0,81,82,83,84,86,87,88,90,91,93,94,95,99,100,151,152,153],[0,82,83,84,85,87,88,89,91,92,94,95,96,100,101,151,152,153],[0,79,80,81,82,83,90,91,95,96,98,101,151,152,153],[0,79,83,85,86,88,89,93,96,98,99,151,152,153],[0,80,84,86,87,89,90,94,97,99,100,151,152,153],[0,81,85,87,88,90,91,95,98,100,101,151,152,153],[0,79,80,81,84,85,93,96,97,98,99,101,151,152,153],[0,79,84,88,89,91,92,93,94,99,100,151,152,153],[0,80,85,89,90,92,93,94,95,100,101,151,152,153],[0,79,80,82,84,85,88,89,90,92,94,95,96,97,98,101,151,152,153],[0,79,82,83,84,88,90,92,95,96,99,151,152,153],[0,80,83,84,85,89,91,93,96,97,100,151,152,153],[0,81,84,85,86,90,92,94,97,98,101,151,152,153],[0,79,80,81,84,87,88,89,92,95,97,99,151,152,153],[0,80,81,82,85,88,89,90,93,96,98,100,151,152,153],[0,81,82,83,86,89,90,91,94,97,99,101,151,152,153],[0,79,80,81,83,85,86,87,88,89,90,93,95,97,100,151,152,153],[0,80,81,82,84,86,87,88,89,90,91,94,96,98,101,151,152,153],[0,79,80,83,84,86,87,90,93,95,98,99,151,152,153],[0,80,81,84,85,87,88,91,94,96,99,100,151,152,153],[0,81,82,85,86,88,89,92,95,97,100,101,151,152,153],[0,79,80,81,83,84,85,87,88,90,91,92,96,97,101,151,152,153],[0,79,151,152,153],[0,80,151,152,153],[0,81,151,152,153],[0,82,151,152,153],[0,83,151,152,153],[0,84,151,152,153],[0,85,151,152,153],[0,86,151,152,153],[0,87,151,152,153],[0,88,151,152,153],[0,89,151,152,153],[0,90,151,152,153],[0,91,151,152,153],[0,92,151,152,153],[0,93,151,152,153],[0,94,151,152,153],[0,95,151,152,153],[0,96,151,152,153],[0,97,151,152,153],[0,98,151,152,153],[0,99,151,152,153],[0,100,151,152,153],[0,101,151,152,153],[0,102,103,104,105,107,108,109,111,112,114,115,116,120,121,151,152,153],[0,103,104,105,106,108,109,110,112,113,115,116,117,121,122,151,152,153],[0,104,105,106,107,109,110,111,113,114,116,117,118,122,123,151,152,153],[0,105,106,107,108,110,111,112,114,115,117,118,119,123,124,151,152,153],[0,102,103,104,105,106,113,114,118,119,121,124,151,152,153],[0,102,106,108,109,111,112,116,119,121,122,151,152,153],[0,103,107,109,110,112,113,117,120,122,123,151,152,153],[0,104,108,110,111,113,114,118,121,123,124,151,152,153],[0,102,103,104,107,108,116,119,120,121,122,124,151,152,153],[0,102,107,111,112,114,115,116,117,122,123,151,152,153],[0,103,108,112,113,115,116,117,118,123,124,151,152,153],[0,102,103,105,107,108,111,112,113,115,117,118,119,120,121,124,151,152,153],[0,102,105,106,107,111,113,115,118,119,122,151,152,153],[0,103,106,107,108,112,114,116,119,120,123,151,152,153],[0,104,107,108,109,113,115,117,120,121,124,151,152,153],[0,102,103,104,107,110,111,112,115,118,120,122,151,152,153],[0,103,104,105,108,111,112,113,116,119,121,123,151,152,153],[0,104,105,106,109,112,113,114,117,120,122,124,151,152,153],[0,102,103,104,106,108,109,110,111,112,113,116,118,120,123,151,152,153],[0,103,104,105,107,109,110,111,112,113,114,117,119,121,124,151,152,153],[0,102,103,106,107,109,110,113,116,118,121,122,151,152,153],[0,103,104,107,108,110,111,114,117,119,122,123,151,152,153],[0,104,105,108,109,111,112,115,118,120,123,124,151,152,153],[0,102,103,104,106,107,108,110,111,113,114,115,119,120,124,151,152,153],[0,102,151,152,153],[0,103,151,152,153],[0,104,151,152,153],[0,105,151,152,153],[0,106,151,152,153],[0,107,151,152,153],[0,108,151,152,153],[0,109,151,152,153],[0,110,151,152,153],[0,111,151,152,153],[0,112,151,152,153],[0,113,151,152,153],[0,114,151,152,153],[0,115,151,152,153],[0,116,151,152,153],[0,117,151,152,153],[0,118,151,152,153],[0,119,151,152,153],[0,120,151,152,153],[0,121,151,152,153],[0,122,151,152,153],[0,123,151,152,153],[0,124,151,152,153],[0,102,103,104,105,107,108,109,111,112,114,115,116,120,121,150,151,152,153],[0,103,104,105,106,108,109,110,112,113,115,116,117,121,122,150,151,152,153],[0,104,105,106,107,109,110,111,113,114,116,117,118,122,123,150,151,152,153],[0,105,106,107,108,110,111,112,114,115,117,118,119,123,124,150,151,152,153],[0,102,103,104,105,106,113,114,118,119,121,124,150,151,152,153],[0,102,106,108,109,111,112,116,119,121,122,150,151,152,153],[0,103,107,109,110,112,113,117,120,122,123,150,151,152,153],[0,104,108,110,111,113,114,118,121,123,124,150,151,152,153],[0,102,103,104,107,108,116,119,120,121,122,124,150,151,152,153],[0,102,107,111,112,114,115,116,117,122,123,150,151,152,153],[0,103,108,112,113,115,116,117,118,123,124,150,151,152,153],[0,102,103,105,107,108,111,112,113,115,117,118,119,120,121,124,150,151,152,153],[0,102,105,106,107,111,113,115,118,119,122,150,151,152,153],[0,103,106,107,108,112,114,116,119,120,123,150,151,152,153],[0,104,107,108,109,113,115,117,120,121,124,150,151,152,153],[0,102,103,104,107,110,111,112,115,118,120,122,150,151,152,153],[0,103,104,105,108,111,112,113,116,119,121,123,150,151,152,153],[0,104,105,106,109,112,113,114,117,120,122,124,150,151,152,153],[0,102,103,104,106,108,109,110,111,112,113,116,118,120,123,150,151,152,153],[0,103,104,105,107,109,110,111,112,113,114,117,119,121,124,150,151,152,153],[0,102,103,106,107,109,110,113,116,118,121,122,150,151,152,153],[0,103,104,107,108,110,111,114,117,119,122,123,150,151,152,153],[0,104,105,108,109,111,112,115,118,120,123,124,150,151,152,153],[0,102,103,104,106,107,108,110,111,113,114,115,119,120,124,150,151,152,153],[0,102,150,151,152,153],[0,103,150,151,152,153],[0,104,150,151,152,153],[0,105,150,151,152,153],[0,106,150,151,152,153],[0,107,150,151,152,153],[0,108,150,151,152,153],[0,109,150,151,152,153],[0,110,150,151,152,153],[0,111,150,151,152,153],[0,112,150,151,152,153],[0,113,150,151,152,153],[0,114,150,151,152,153],[0,115,150,151,152,153],[0,116,150,151,152,153],[0,117,150,151,152,153],[0,118,150,151,152,153],[0,119,150,151,152,153],[0,120,150,151,152,153],[0,121,150,151,152,153],[0,122,150,151,152,153],[0,123,150,151,152,153],[0,124,150,151,152,153],[0,125,126,130,131,132,134,150,151,152,153],[0,126,127,131,132,133,135,150,151,152,153],[0,125,126,127,128,130,131,133,150,151,152,153],[0,126,127,128,129,131,132,134,150,151,152,153],[0,127,128,129,130,132,133,135,150,151,152,153],[0,125,126,128,129,132,133,150,151,152,153],[0,126,127,129,130,133,134,150,151,152,153],[0,127,128,130,131,134,135,150,151,152,153],[0,125,126,128,129,130,134,135,150,151,152,153],[0,125,127,129,132,134,135,150,151,152,153],[0,125,128,131,132,133,134,135,150,151,152,153],[0,125,129,130,131,133,135,150,151,152,153],[0,125,150,151,152,153],[0,126,150,151,152,153],[0,127,150,151,152,153],[0,128,150,151,152,153],[0,129,150,151,152,153],[0,130,150,151,152,153],[0,131,150,151,152,153],[0,132,150,151,152,153],[0,133,150,151,152,153],[0,134,150,151,152,153],[0,135,150,151,152,153],[0,125,126,130,131,132,134,149,150,151,152,153],[0,126,127,131,132,133,135,149,150,151,152,153],[0,125,126,127,128,130,131,133,149,150,151,152,153],[0,126,127,128,129,131,132,134,149,150,151,152,153],[0,127,128,129,130,132,133,135,149,150,151,152,153],[0,125,126,128,129,132,133,149,150,151,152,153],[0,126,127,129,130,133,134,149,150,151,152,153],[0,127,128,130,131,134,135,149,150,151,152,153],[0,125,126,128,129,130,134,135,149,150,151,152,153],[0,125,127,129,132,134,135,149,150,151,152,153],[0,125,128,131,132,133,134,135,149,150,151,152,153],[0,125,129,130,131,133,135,149,150,151,152,153],[0,125,149,150,151,152,153],[0,126,149,150,151,152,153],[0,127,149,150,151,152,153],[0,128,149,150,151,152,153],[0,129,149,150,151,152,153],[0,130,149,150,151,152,153],[0,131,149,150,151,152,153],[0,132,149,150,151,152,153],[0,133,149,150,151,152,153],[0,134,149,150,151,152,153],[0,135,149,150,151,152,153],[0,137,143,149,150,151,152,153],[0,136,142,143,149,150,151,152,153],[0,136,142,149,150,151,152,153],[0,141,143,149,150,151,152,153],[0,137,138,140,149,150,151,152,153],[0,141,142,149,150,151,152,153],[0,139,143,149,150,151,152,153],[0,136,139,143,149,150,151,152,153],[0,136,139,149,150,151,152,153],[0,138,140,149,150,151,152,153],[0,138,149,150,151,152,153],[0,141,149,150,151,152,153],[0,141,142,143,149,150,151,152,153],[0,137,138,149,150,151,152,153],[0,139,149,150,151,152,153],[0,140,143,149,150,151,152,153],[0,137,140,143,149,150,151,152,153],[0,137,143,148,149,150,151,152,153],[0,136,142,143,148,149,150,151,152,153],[0,136,142,148,149,150,151,152,153],[0,141,143,148,149,150,151,152,153],[0,137,138,140,148,149,150,151,152,153],[0,141,142,148,149,150,151,152,153],[0,139,143,148,149,150,151,152,153],[0,136,139,143,148,149,150,151,152,153],[0,136,139,148,149,150,151,152,153],[0,138,140,148,149,150,151,152,153],[0,138,148,149,150,151,152,153],[0,141,148,149,150,151,152,153],[0,141,142,143,148,149,150,151,152,153],[0,137,138,148,149,150,151,152,153],[0,139,148,149,150,151,152,153],[0,140,143,148,149,150,151,152,153],[0,137,140,143,148,149,150,151,152,153],[0,144,145,148,149,150,151,152,153],[0,145,146,148,149,150,151,152,153],[0,144,145,146,148,149,150,151,152,153],[0,144,146,148,149,150,151,152,153],[0,144,148,149,150,151,152,153],[0,145,148,149,150,151,152,153],[0,146,148,149,150,151,152,153],[0,144,145,147,148,149,150,151,152,153],[0,145,146,147,148,149,150,151,152,153],[0,144,145,146,147,148,149,150,151,152,153],[0,144,146,147,148,149,150,151,152,153],[0,144,147,148,149,150,151,152,153],[0,145,147,148,149,150,151,152,153],[0,146,147,148,149,150,151,152,153],[0,147,148,149,150,151,152,153]]},"distance":{"d":6,"is_exact":false,"upper":15,"witness":[0,79,158,237,316,363,410,457,504,527,550,567,584,591,598],"A_d":null,"certified":{"d":15,"is_exact":false,"met":true,"source":"Jain and Albert (arXiv:2408.12752), Table II: [[79,1,15]] quantum QR code (extended QR [80,40,16]) doubled onto [[441,1,13]]; 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)"}},"clifford":{"kind":"powers","correction":{"S":[[0,1],[150,1],[151,2],[152,3]],"CZ":[[0,150],[0,152],[150,151],[150,152],[150,153],[152,153]]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[7,7],[8,7],[9,7],[10,7],[11,7],[12,7],[13,7],[14,7],[15,7],[16,7],[17,7],[18,7],[19,7],[20,7],[21,7],[22,7],[23,7],[24,7],[25,7],[26,7],[27,7],[28,7],[29,7],[30,7],[31,7],[32,7],[33,7],[34,7],[35,7],[36,7],[37,7],[38,7],[39,7],[40,7],[41,7],[42,7],[43,7],[44,7],[45,7],[46,7],[47,7],[48,7],[49,7],[50,7],[51,7],[52,7],[53,7],[54,7],[55,7],[56,7],[57,7],[58,7],[59,7],[60,7],[61,7],[62,7],[63,7],[64,7],[65,7],[66,7],[67,7],[68,7],[69,7],[70,7],[71,7],[72,7],[73,7],[74,7],[75,7],[76,7],[77,7],[78,7],[79,7],[80,7],[81,7],[82,7],[83,7],[84,7],[85,7],[86,7],[87,7],[88,7],[89,7],[90,7],[91,7],[92,7],[93,7],[94,7],[95,7],[96,7],[97,7],[98,7],[99,7],[100,7],[101,7],[102,7],[103,7],[104,7],[105,7],[106,7],[107,7],[108,7],[109,7],[110,7],[111,7],[112,7],[113,7],[114,7],[115,7],[116,7],[117,7],[118,7],[119,7],[120,7],[121,7],[122,7],[123,7],[124,7],[125,7],[126,7],[127,7],[128,7],[129,7],[130,7],[131,7],[132,7],[133,7],[134,7],[135,7],[136,7],[137,7],[138,7],[139,7],[140,7],[141,7],[142,7],[143,7],[144,7],[145,7],[146,7],[147,7],[148,7],[149,7],[150,7],[151,7],[152,7],[153,7],[154,7],[155,7],[156,7],[157,7],[316,7],[317,7],[318,7],[319,7],[320,7],[321,7],[322,7],[323,7],[324,7],[325,7],[326,7],[327,7],[328,7],[329,7],[330,7],[331,7],[332,7],[333,7],[334,7],[335,7],[336,7],[337,7],[338,7],[339,7],[340,7],[341,7],[342,7],[343,7],[344,7],[345,7],[346,7],[347,7],[348,7],[349,7],[350,7],[351,7],[352,7],[353,7],[354,7],[355,7],[356,7],[357,7],[358,7],[359,7],[360,7],[361,7],[362,7],[363,7],[364,7],[365,7],[366,7],[367,7],[368,7],[369,7],[370,7],[371,7],[372,7],[373,7],[374,7],[375,7],[376,7],[377,7],[378,7],[379,7],[380,7],[381,7],[382,7],[383,7],[384,7],[385,7],[386,7],[387,7],[388,7],[389,7],[390,7],[391,7],[392,7],[393,7],[394,7],[395,7],[396,7],[397,7],[398,7],[399,7],[400,7],[401,7],[402,7],[403,7],[404,7],[405,7],[406,7],[407,7],[408,7],[409,7],[504,7],[505,7],[506,7],[507,7],[508,7],[509,7],[510,7],[511,7],[512,7],[513,7],[514,7],[515,7],[516,7],[517,7],[518,7],[519,7],[520,7],[521,7],[522,7],[523,7],[524,7],[525,7],[526,7],[527,7],[528,7],[529,7],[530,7],[531,7],[532,7],[533,7],[534,7],[535,7],[536,7],[537,7],[538,7],[539,7],[540,7],[541,7],[542,7],[543,7],[544,7],[545,7],[546,7],[547,7],[548,7],[549,7],[550,7],[551,7],[552,7],[553,7],[554,7],[555,7],[556,7],[557,7],[558,7],[559,7],[560,7],[561,7],[562,7],[563,7],[564,7],[565,7],[566,7],[567,7],[568,7],[569,7],[570,7],[571,7],[572,7],[573,7],[574,7],[575,7],[576,7],[577,7],[578,7],[579,7],[580,7],[581,7],[582,7],[583,7],[584,7],[585,7],[586,7],[587,7],[588,7],[589,7],[590,7],[591,7],[592,7],[593,7],[594,7],[595,7],[596,7],[597,7],[598,7]]},"metrics":{"gamma":3.5692634574833444,"gamma_t":3.5692634574833444,"gamma_rho":3.5692634574833444,"gamma_claim":2.3615742409474163,"gamma_t_claim":2.3615742409474163,"gamma_rho_claim":2.3615742409474163,"v_ex":1,"rate":0.001669449081803005,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Jain-Albert doubling: weak triply even family"],"discovery":"pre-existing","strongest_claim":"a code of the weak triply even family of Jain and Albert (arXiv:2408.12752, Table II; transversal_t_codes/): quadratic-residue CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction, where T on some qubits and T-dagger on the rest is a logical T; a verified witness, not a maximum","sources":[{"regime":"Jain-Albert doubling: weak triply even family","file":"transversal_t_codes/factories.json","label":"JA-599","N":154,"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 [[441,1,13]] (Table II)"}]},"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"}]}