Best Known (3, 3+56, s)-Nets in Base 25
(3, 3+56, 52)-Net over F25 — Constructive and digital
Digital (3, 59, 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+56, 56)-Net over F25 — Digital
Digital (3, 59, 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+56, 270)-Net in Base 25 — Upper bound on s
There is no (3, 59, 271)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2559, 271, S25, 56), but
- the linear programming bound shows that M ≥ 3469 759982 677660 667816 934330 536314 687351 703098 477714 871216 697179 354365 547510 052891 766463 289968 669414 520263 671875 / 112434 676287 209700 530106 873307 > 2559 [i]