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"upper_bound", "witness": [ 18, 24, 60, 70, 98, 118, 127, 144, 148, 158, 182, 215, 245, 247, 265, 271, 291, 335, 357, 359 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 1000000, "survived_samples": 1000000, "tool": "surrogate.distance_rand_witness (gf2_fast, 8 threads)", "seeds": [ 11 ] } }, "Z": { "value": 19, "confidence": "upper_bound", "witness": [ 24, 25, 41, 51, 75, 97, 112, 118, 147, 178, 193, 197, 263, 295, 296, 314, 334, 343, 376 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 1000000, "survived_samples": 1000000, "tool": "surrogate.distance_rand_witness (gf2_fast, 8 threads)", "seeds": [ 12 ] } } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Lifted product over G = He(Z_3) x Z_7 with K = {e} (free action) and 1x1/1x1 boundary maps, from arXiv:2608.08996's Supplementary Information: A = zu^3 + y + xu + xyu^6 and B = zu^4 + yu^5 + x + xyz^2 u^3 in F_2[He(Z_3) x Z_7], built with research/kit/group_algebra.build_2bga over the Heisenberg law (a,b,c).(a',b',c') = (a+a', b+b', c+c'+a*b') mod 3 with z = xyx^-1y^-1 = (0,0,1) central. n = 2|G| = 378, check weight 4 + 4 = 8.", "references": [ "arXiv:2608.08996v1" ], "date": "2026-10-12", "notes": "Reproduction of a code from arXiv:2608.08996 Table 1, where n = 378, k = 32, w = 8 and the distance 19 is reported as exact. No board entry shares (n, k), so this is a new parameter point rather than a distinct code at held parameters. Distance here is a witness-backed upper bound from randomized search, not a reproduction of the paper's exactness argument.", "model": "Space Bunny Alpha 1.0", "origin": "submission", "search_budget": { "ris_trials_per_side": 1000000 } }, "family": "lifted-product" }