{"id":"185.1.7.a","row":815,"stored":{"file":"master_catalog.json","row":815,"construction":null,"columns_sha256":null},"parameters":{"n":185,"k":1,"d":7,"N":49,"r":48,"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":[[0,1,2,3,7,14,16,18,21],[0,1,3,6,10,11,13,16,17,18,20,21,22],[0,1,6,7,8,10,12,13,14,15,16,17,20,22],[0,5,6,7,8,10,11,12,14,15,17,18,19],[0,1,2,3,6,8,9,11,12,13,14,15,19,20,21],[0,1,2,4,5,6,15,16,18,19,20,21,22],[0,1,3,4,5,7,8,10,11,13,15,17,18,22],[0,4,8,10,11,13,14,18,21],[0,1,2,3,5,7,9,11,12,15,16,18,19,21,22],[0,1,2,4,5,7,8,9,14,16,17,18,20,22],[0,3,8,12,13,15,16,17,18],[0,1,2,3,4,7,9,13,17,19,21],[0,1,2,4,6,7,8,9,12,13,19,20,22],[0,1,3,4,5,6,7,9,11,14,15,16,18,19],[0,4,7,8,9,13,15,17,20,21],[0,2,3,4,7,10,11,12,15,18,20,22],[0,3,4,5,8,11,12,13,16,19,21],[0,1,6,8,11,13,14,15,17,18,22],[0,1,2,3,5,6,10,13,15,16],[0,3,4,5,7,9,10,11,12,13,14,17,19,21],[0,2,3,6,7,9,10,13,16,18,21,22],[0,3,4,7,8,10,11,14,17,19,22],[0,1],[0,2,3,4,6,7,8,10,11,13,14,15,19,20],[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],[0,1,2,3,7,14,16,18,21,48],[0,1,3,6,10,11,13,16,17,18,20,21,22,48],[0,1,6,7,8,10,12,13,14,15,16,17,20,22,48],[0,5,6,7,8,10,11,12,14,15,17,18,19,48],[0,1,2,3,6,8,9,11,12,13,14,15,19,20,21,48],[0,1,2,4,5,6,15,16,18,19,20,21,22,48],[0,1,3,4,5,7,8,10,11,13,15,17,18,22,48],[0,4,8,10,11,13,14,18,21,48],[0,1,2,3,5,7,9,11,12,15,16,18,19,21,22,48],[0,1,2,4,5,7,8,9,14,16,17,18,20,22,48],[0,3,8,12,13,15,16,17,18,48],[0,1,2,3,4,7,9,13,17,19,21,48],[0,1,2,4,6,7,8,9,12,13,19,20,22,48],[0,1,3,4,5,6,7,9,11,14,15,16,18,19,48],[0,4,7,8,9,13,15,17,20,21,48],[0,2,3,4,7,10,11,12,15,18,20,22,48],[0,3,4,5,8,11,12,13,16,19,21,48],[0,1,6,8,11,13,14,15,17,18,22,48],[0,1,2,3,5,6,10,13,15,16,48],[0,3,4,5,7,9,10,11,12,13,14,17,19,21,48],[0,2,3,6,7,9,10,13,16,18,21,22,48],[0,3,4,7,8,10,11,14,17,19,22,48],[0,1,48],[0,2,3,4,6,7,8,10,11,13,14,15,19,20,48],[0,2,48],[0,3,48],[0,4,48],[0,5,48],[0,6,48],[0,7,48],[0,8,48],[0,9,48],[0,10,48],[0,11,48],[0,12,48],[0,13,48],[0,14,48],[0,15,48],[0,16,48],[0,17,48],[0,18,48],[0,19,48],[0,20,48],[0,21,48],[0,22,48],[0,23,24,28,29,30,32,48],[0,24,25,29,30,31,33,48],[0,23,24,25,26,28,29,31,48],[0,24,25,26,27,29,30,32,48],[0,25,26,27,28,30,31,33,48],[0,23,24,26,27,30,31,48],[0,24,25,27,28,31,32,48],[0,25,26,28,29,32,33,48],[0,23,24,26,27,28,32,33,48],[0,23,25,27,30,32,33,48],[0,23,26,29,30,31,32,33,48],[0,23,27,28,29,31,33,48],[0,23,48],[0,24,48],[0,25,48],[0,26,48],[0,27,48],[0,28,48],[0,29,48],[0,30,48],[0,31,48],[0,32,48],[0,33,48],[0,23,24,28,29,30,32,47,48],[0,24,25,29,30,31,33,47,48],[0,23,24,25,26,28,29,31,47,48],[0,24,25,26,27,29,30,32,47,48],[0,25,26,27,28,30,31,33,47,48],[0,23,24,26,27,30,31,47,48],[0,24,25,27,28,31,32,47,48],[0,25,26,28,29,32,33,47,48],[0,23,24,26,27,28,32,33,47,48],[0,23,25,27,30,32,33,47,48],[0,23,26,29,30,31,32,33,47,48],[0,23,27,28,29,31,33,47,48],[0,23,47,48],[0,24,47,48],[0,25,47,48],[0,26,47,48],[0,27,47,48],[0,28,47,48],[0,29,47,48],[0,30,47,48],[0,31,47,48],[0,32,47,48],[0,33,47,48],[0,35,41,47,48],[0,34,40,41,47,48],[0,34,40,47,48],[0,39,41,47,48],[0,35,36,38,47,48],[0,39,40,47,48],[0,37,41,47,48],[0,34,37,41,47,48],[0,34,37,47,48],[0,36,38,47,48],[0,36,47,48],[0,39,47,48],[0,39,40,41,47,48],[0,35,36,47,48],[0,37,47,48],[0,38,41,47,48],[0,35,38,41,47,48],[0,35,41,46,47,48],[0,34,40,41,46,47,48],[0,34,40,46,47,48],[0,39,41,46,47,48],[0,35,36,38,46,47,48],[0,39,40,46,47,48],[0,37,41,46,47,48],[0,34,37,41,46,47,48],[0,34,37,46,47,48],[0,36,38,46,47,48],[0,36,46,47,48],[0,39,46,47,48],[0,39,40,41,46,47,48],[0,35,36,46,47,48],[0,37,46,47,48],[0,38,41,46,47,48],[0,35,38,41,46,47,48],[0,42,43,46,47,48],[0,43,44,46,47,48],[0,42,43,44,46,47,48],[0,42,44,46,47,48],[0,42,46,47,48],[0,43,46,47,48],[0,44,46,47,48],[0,42,43,45,46,47,48],[0,43,44,45,46,47,48],[0,42,43,44,45,46,47,48],[0,42,44,45,46,47,48],[0,42,45,46,47,48],[0,43,45,46,47,48],[0,44,45,46,47,48],[0,45,46,47,48]]},"distance":{"d":7,"is_exact":false,"upper":9,"witness":[26,71,93,116,136,147,149,156,163],"A_d":null,"certified":{"d":9,"is_exact":false,"met":true,"source":"Jain and Albert (arXiv:2408.12752), Table I: [[45,1,9]] code of the self-dual [46,23,10] code sub(XQ47) doubled onto [[95,1,7]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 9, with d_sd at least the classical distance less one (their Lemma 2.4)"}},"clifford":{"kind":"powers","correction":{"S":[[1,2],[4,2],[5,2],[8,2],[9,2],[11,2],[12,2],[15,2],[18,2],[20,2],[48,2]],"CZ":[[1,48],[4,48],[5,48],[8,48],[9,48],[11,48],[12,48],[15,48],[18,48],[20,48]]},"rotation_powers":[[2,3],[4,3],[6,3],[8,3],[9,3],[11,3],[13,3],[14,3],[16,3],[17,3],[18,3],[19,3],[21,3],[23,3],[47,3],[49,3],[51,3],[53,3],[54,3],[56,3],[58,3],[59,3],[61,3],[62,3],[63,3],[64,3],[66,3],[68,3]]},"metrics":{"gamma":2.682732205088023,"gamma_t":2.682732205088023,"gamma_rho":2.682732205088023,"gamma_claim":2.3758863244680994,"gamma_t_claim":2.3758863244680994,"gamma_rho_claim":2.3758863244680994,"v_ex":1,"rate":0.005405405405405406,"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-185","N":49,"d":7,"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":"[[45,1,9]] code of the self-dual [46,23,10] code sub(XQ47) doubled onto [[95,1,7]] (Table I)"}]},"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"}]}