Best Known (62−59, 62, s)-Nets in Base 25
(62−59, 62, 52)-Net over F25 — Constructive and digital
Digital (3, 62, 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
(62−59, 62, 56)-Net over F25 — Digital
Digital (3, 62, 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
(62−59, 62, 243)-Net in Base 25 — Upper bound on s
There is no (3, 62, 244)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2562, 244, S25, 59), but
- the linear programming bound shows that M ≥ 70231 469910 639265 862630 211027 901425 927817 325397 443460 018250 685054 990560 754885 169092 442964 711153 763346 374034 881591 796875 / 143 765455 317640 678369 295295 721163 > 2562 [i]