Best Known (21−20, 21, s)-Nets in Base 25
(21−20, 21, 27)-Net over F25 — Constructive and digital
Digital (1, 21, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
(21−20, 21, 36)-Net over F25 — Digital
Digital (1, 21, 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
(21−20, 21, 123)-Net in Base 25 — Upper bound on s
There is no (1, 21, 124)-net in base 25, because
- 12 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