Best Known (1, 1+24, s)-Nets in Base 25
(1, 1+24, 27)-Net over F25 — Constructive and digital
Digital (1, 25, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
(1, 1+24, 36)-Net over F25 — Digital
Digital (1, 25, 36)-net over F25, using
- net from sequence [i] based on digital (1, 35)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 1 and N(F) ≥ 36, using
(1, 1+24, 93)-Net over F25 — Upper bound on s (digital)
There is no digital (1, 25, 94)-net over F25, because
- extracting embedded orthogonal array [i] would yield linear OA(2525, 94, F25, 24) (dual of [94, 69, 25]-code), but
- construction Y1 [i] would yield
- linear OA(2524, 27, F25, 24) (dual of [27, 3, 25]-code or 27-arc in PG(23,25)), but
- OA(2569, 94, S25, 67), but
- discarding factors 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]
- discarding factors would yield OA(2569, 73, S25, 67), but
- construction Y1 [i] would yield
(1, 1+24, 123)-Net in Base 25 — Upper bound on s
There is no (1, 25, 124)-net in base 25, because
- 16 times m-reduction [i] would yield (1, 9, 124)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(259, 124, S25, 8), but
- the linear programming bound shows that M ≥ 119725 208199 920654 296875 / 31015 449154 > 259 [i]
- extracting embedded orthogonal array [i] would yield OA(259, 124, S25, 8), but