Best Known (58−39, 58, s)-Nets in Base 25
(58−39, 58, 148)-Net over F25 — Constructive and digital
Digital (19, 58, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
(58−39, 58, 162)-Net over F25 — Digital
Digital (19, 58, 162)-net over F25, using
- net from sequence [i] based on digital (19, 161)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 162, using
(58−39, 58, 5152)-Net in Base 25 — Upper bound on s
There is no (19, 58, 5153)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 57, 5153)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 48 274684 041919 872828 361618 411371 917752 144055 277261 718967 920295 490517 943891 756425 > 2557 [i]