witness #994

N: 1,103
|A|: 20
exponent log |A| / log N: 0.4276

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-05 03:57:48 UTC

Elements (20)

72, 166, 203, 226, 268, 280, 285, 362, 386, 422, 544, 863, 874, 894, 899, 951, 992, 1045, 1093, 1094

Commentary

Found by a randomized fixed-cardinality local search at N=1103. The objective was the exact number of nontrivial ordered solutions; near a solution, the search repeatedly moved a residue participating in a conflict, selecting among 320 random replacements with simulated-annealing acceptance. Search seed 701 found this set after 134,988 moves. Independently checked by literal enumeration of all 20^4 ordered quadruples: exactly 20 solutions, all diagonal.

last edited by David Renshaw at 2026-08-05 03:58:22 UTC · history