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195, 202, 203, 211, 216, 225, 234, 239, 243, 267, 275, 289, 294, 295, 304, 307, 318, 326, 336, 337 ] }, "Z": { "value": 34, "confidence": "upper_bound", "witness": [ 3, 23, 30, 32, 34, 42, 54, 57, 62, 69, 72, 94, 104, 112, 130, 132, 142, 145, 192, 193, 215, 221, 226, 232, 260, 273, 292, 293, 294, 313, 321, 322, 334, 340 ] } }, "family": "lifted-product", "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group algebra code over the dihedral group D87 (order 174): HX = [L[a] L[b]], HZ = [R[b] R[a]] with element-index supports a=[54, 62, 94], b=[2, 51, 56, 88, 118, 161, 168] in the left/right regular representation; n = 2|G|, max check weight 10.", "references": [], "date": "2026-08-07", "notes": "Found by a MAP-Elites search over non-abelian 2BGA codes gated by an escalating distance ladder; the reported d is the minimum over multi-seed randomized information-set searches at 200k, 2M and 20M iterations (values agreed across all rungs), with the recorded per-side witnesses extracted at the 20M budget.", "model": "Claude Opus 5" } }