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    82,
    94,
    128,
    142,
    172
   ],
   [
    9,
    23,
    83,
    88,
    143,
    160,
    165,
    173
   ],
   [
    11,
    24,
    26,
    84,
    92,
    128,
    174,
    176
   ],
   [
    29,
    30,
    67,
    85,
    97,
    104,
    133,
    175
   ],
   [
    15,
    31,
    86,
    89,
    134,
    171,
    175,
    176
   ],
   [
    17,
    32,
    34,
    87,
    106,
    137,
    173,
    177
   ],
   [
    22,
    38,
    40,
    88,
    98,
    103,
    159,
    178
   ],
   [
    30,
    47,
    49,
    89,
    109,
    119,
    151,
    179
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    19,
    53,
    78,
    80,
    109,
    114,
    119,
    122,
    146,
    149,
    154,
    158,
    167,
    170
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1014
    ]
   }
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    40,
    41,
    43,
    44,
    47,
    50,
    72,
    73,
    78,
    88,
    103,
    114,
    134,
    178
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1015
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C15 x S3 = SmallGroup(90, 6) (order 90), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 180; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 9, 12, 65}, b = {0, 3, 71, 83} as element indices. Check weight 8. 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"
}