Best Known (58−55, 58, s)-Nets in Base 25
(58−55, 58, 52)-Net over F25 — Constructive and digital
Digital (3, 58, 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
(58−55, 58, 56)-Net over F25 — Digital
Digital (3, 58, 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
(58−55, 58, 274)-Net in Base 25 — Upper bound on s
There is no (3, 58, 275)-net in base 25, because
- 9 times m-reduction [i] would yield (3, 49, 275)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(2549, 275, S25, 46), but
- the linear programming bound shows that M ≥ 6 430313 750241 332147 612039 871646 663038 243180 749329 590988 917770 832955 511650 652624 666690 826416 015625 / 20311 023951 484409 636688 674357 > 2549 [i]
- extracting embedded orthogonal array [i] would yield OA(2549, 275, S25, 46), but