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   ]
  ]
 },
 "distance": {
  "d": 18,
  "X": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    2,
    14,
    32,
    38,
    41,
    47,
    50,
    62,
    80,
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    137,
    143
   ]
  },
  "Z": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
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    160,
    163,
    166,
    169,
    187,
    199,
    208,
    211,
    214,
    217,
    235,
    247,
    256,
    259,
    262,
    265,
    283
   ]
  }
 },
 "provenance": {
  "authors": [
   "Qian, Dongheng",
   "Li, Tianyi"
  ],
  "construction": "Lifted product (2BGA) over Z_12 x Z_12, reconstructed from arXiv:2608.08996 Table 1 (coset-orbit balanced product over Z_12 x Z_48 with normal stabilizer K=<y^12>, reduced to G/K). A = y^2 + y^7 + x, B = y^3 + x + x^2 + x^5 y^9. n=2*12*12=288.",
  "references": [
   "arXiv:2608.08996"
  ],
  "date": "2026",
  "notes": "Literature baseline. Reconstructed from the paper's published construction data (Table 1, w=7): the balanced product over Z_12 x Z_48 with normal stabilizer K=<y^12> reduces to a lifted product over G/K = Z_12 x Z_12, with A = y^2 + y^7 + x and B = y^3 + x + x^2 + x^5 y^9 (y-exponents reduced mod 12). Paper reports d = 18 as MILP-exact; here recorded as a witness-backed upper bound (not server-certified).",
  "origin": "baseline"
 },
 "family": "lifted-product"
}
