Best Known (2, 2+∞, s)-Nets in Base 25
(2, 2+∞, 28)-Net over F25 — Constructive and digital
Digital (2, m, 28)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
(2, 2+∞, 46)-Net over F25 — Digital
Digital (2, m, 46)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 45)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 2 and N(F) ≥ 46, using
(2, 2+∞, 72)-Net in Base 25 — Upper bound on s
There is no (2, m, 73)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (2, 69, 73)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(2569, 73, S25, 67), but
- the linear programming bound shows that M ≥ 24178 564222 846123 668546 399721 917528 895562 151649 914153 732205 158997 548011 257094 913162 291049 957275 390625 / 7242 > 2569 [i]
- extracting embedded orthogonal array [i] would yield OA(2569, 73, S25, 67), but