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and Albert (arXiv:2408.12752), Table I: [[47,1,11]] quantum QR code (extended QR [48,24,12]) doubled onto [[185,1,9]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 11, with d_sd at least the classical distance less one (their Lemma 2.4)"}},"clifford":{"kind":"powers","correction":{"S":[[0,1],[24,2],[27,2],[28,2],[31,2],[32,2],[34,2],[35,2],[38,2],[41,2],[43,2],[71,2]],"CZ":[[24,71],[27,71],[28,71],[31,71],[32,71],[34,71],[35,71],[38,71],[41,71],[43,71]]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[5,7],[6,7],[7,7],[9,7],[10,7],[12,7],[13,7],[14,7],[18,7],[19,7],[23,7],[51,3],[55,3],[58,3],[62,3],[63,3],[64,3],[67,3],[68,3],[69,3],[71,3],[72,3],[73,3],[74,3],[75,3],[76,3],[77,3],[78,3],[79,3],[80,3],[81,3],[82,3],[83,3],[84,3],[85,3],[86,3],[87,3],[88,3],[89,3],[90,3],[91,3],[92,3],[93,3],[95,3],[98,3],[99,3],[105,3],[106,3],[107,3],[108,3],[109,3],[110,3],[112,3],[113,3],[114,3],[117,3],[138,3],[139,3],[141,3],[142,3],[145,3],[146,3],[147,3],[148,3],[149,3],[156,3],[160,3],[161,3],[163,3],[164,3],[165,3],[166,3],[167,3],[168,3],[169,3],[170,3],[171,3],[172,3],[173,3],[174,3],[175,3],[176,3],[177,3],[178,3],[179,3],[180,3],[181,3],[182,3],[184,3],[188,3],[189,3],[190,3],[192,3],[194,3],[206,3],[207,3],[211,3],[212,3],[213,3],[215,3],[217,3],[229,3],[231,3],[232,3],[234,3],[240,3],[246,3],[247,3],[250,3],[252,3],[253,3],[254,3],[255,3],[256,3],[258,3],[259,3],[260,3],[261,3],[262,3]]},"metrics":{"gamma":2.89387040021101,"gamma_t":2.89387040021101,"gamma_rho":2.89387040021101,"gamma_claim":2.348397715989355,"gamma_t_claim":2.348397715989355,"gamma_rho_claim":2.348397715989355,"v_ex":1,"rate":0.0035842293906810036,"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-279","N":73,"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":"[[47,1,11]] quantum QR code (extended QR [48,24,12]) doubled onto [[185,1,9]] (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"}]}