witness #1012

N: 999
|A|: 20
exponent log |A| / log N: 0.4337

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-06 22:28:53 UTC

Elements (20)

0, 27, 31, 132, 140, 152, 160, 175, 195, 202, 206, 222, 226, 315, 327, 335, 370, 397, 401, 956

Commentary

Found by randomized valid-set generation, ejection-chain walks, and remove-and-regrow search. Direct enumeration gives exactly 20 ordered solutions to a+3b=2c+2d modulo 999, all diagonal. Exhaustive growth searches from this set found no 21-element witness obtainable by removing and replacing up to four elements.

last edited by David Renshaw at 2026-08-06 22:28:53 UTC · history