witness #1989

N: 18,750
|A|: 100
exponent log |A| / log N: 0.4681

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-09 10:30:15 UTC

Elements (100)

5, 11, 20, 30, 36, 120, 130, 136, 145, 155, 161, 756, 758, 781, 783, 881, 883, 906, 908, 2255, 2280, 2380, 2405, 3751, 3755, 3760, 3761, 3776, 3780, 3785, 3786, 3876, 3880, 3885, 3886, 3901, 3905, 3910, 3911, 4501, 4526, 4626, 4651, 6005, 6030, 6130, 6155, 8253, 8258, 8261, 8278, 8283, 8286, 8378, 8383, 8386, 8403, 8408, 8411, 9760, 9785, 9885, 9910, 11260, 11285, 11385, 11410, 11993, 12003, 12011, 12018, 12028, 12036, 12118, 12128, 12136, 12143, 12153, 12161, 13495, 13520, 13620, 13645, 15001, 15006, 15026, 15031, 15126, 15131, 15151, 15156, 15751, 15776, 15876, 15901, 17260, 17285, 17385, 17410, 18745

Commentary

From the N=3525 record (47 points), write N=25q with q=141. In the natural uq+v coordinates, 44/47 points form pairs separated by 25; completing the three missing partners gives a 50-point code C+25{0,1}, where C is a 25-point core. The core has the stronger property that the only solutions to the genus-one relation in (Z/25Z)^2 are diagonal, so it can be amplified by the base-5 integer code T2={0,1,5,6}: A_q={uq+v+25t:(u,v) in C,t in T2}. The vertical width is 168, hence this 100-point family is valid for every q>=673 (and exceptionally q=669). This submission is q=750.

last edited by Yongxi (Aaron) Lin at 2026-08-09 10:30:15 UTC · history