Best Known (3, 3+37, s)-Nets in Base 25
(3, 3+37, 52)-Net over F25 — Constructive and digital
Digital (3, 40, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
(3, 3+37, 56)-Net over F25 — Digital
Digital (3, 40, 56)-net over F25, using
- net from sequence [i] based on digital (3, 55)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 56, using
(3, 3+37, 296)-Net in Base 25 — Upper bound on s
There is no (3, 40, 297)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2540, 297, S25, 37), but
- the linear programming bound shows that M ≥ 14 877320 808563 867564 102762 893164 124779 858681 346667 026446 084491 908550 262451 171875 000000 / 179348 131546 674582 363935 670083 > 2540 [i]