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"value": 16, "confidence": "upper_bound", "witness": [ 20, 21, 33, 37, 69, 83, 93, 102, 158, 164, 199, 213, 246, 257, 262, 274 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1038 ] } }, "Z": { "value": 16, "confidence": "upper_bound", "witness": [ 4, 25, 36, 42, 60, 68, 84, 123, 169, 180, 187, 194, 211, 235, 256, 267 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1039 ] } } }, "provenance": { "authors": [ "Lee, Gideon" ], "construction": "Two-block group-algebra code C(a,b) over C3 x (C3 : C16) = SmallGroup(144, 28) (order 144), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 288; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 7, 39}, b = {0, 10} as element indices. Check weight 5. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.", "references": [ "arXiv:2610.13880" ], "date": "2026-10-12", "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.", "origin": "baseline", "novelty": "known_parameters", "model": "Mimo-V2.6-Flash" }, "family": "2bga-nonabelian" }