witness #2259

N: 31,250
|A|: 123
exponent log |A| / log N: 0.4650

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-09 23:36:11 UTC

Elements (123)

0, 3, 13, 50, 53, 63, 251, 301, 510, 511, 560, 561, 1258, 1260, 1263, 1308, 1310, 1313, 2510, 2560, 2751, 2761, 2801, 2811, 3000, 3001, 3005, 3011, 3050, 3051, 3055, 3061, 3750, 3753, 3800, 3803, 4006, 4011, 4056, 4061, 4250, 4251, 4256, 4260, 4300, 4301, 4306, 4310, 5005, 5055, 6275, 6278, 6288, 6300, 6303, 6526, 6551, 6785, 6786, 6810, 6811, 7533, 7535, 7538, 7558, 7560, 8785, 8810, 9026, 9036, 9051, 9061, 9275, 9276, 9280, 9286, 9300, 9301, 9305, 9311, 10025, 10028, 10050, 10053, 10281, 10286, 10306, 10311, 10525, 10526, 10531, 10535, 10550, 10551, 10556, 10560, 11280, 11305, 18750, 18753, 18763, 19001, 19260, 19261, 20008, 20010, 20013, 21260, 21501, 21511, 21750, 21751, 21755, 21761, 22500, 22503, 22756, 22761, 23000, 23001, 23006, 23010, 23755

Commentary

Same N=3750 hidden-core construction. The 25-point core has optimal vertical span 13; fiber-lift by an exact five-point Z/5 code to a 125-point exact code mod 125, then optimize horizontal shear and high digit at q=250. The resulting conflict hypergraph has a two-point transversal; deleting 7563 and 6313 gives 123 points, improving the previous 121 record.

last edited by Yongxi (Aaron) Lin at 2026-08-09 23:36:11 UTC · history