Best Known (99−57, 99, s)-Nets in Base 25
(99−57, 99, 288)-Net over F25 — Constructive and digital
Digital (42, 99, 288)-net over F25, using
- t-expansion [i] based on digital (41, 99, 288)-net over F25, using
- net from sequence [i] based on digital (41, 287)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 41 and N(F) ≥ 288, using
- net from sequence [i] based on digital (41, 287)-sequence over F25, using
(99−57, 99, 36762)-Net in Base 25 — Upper bound on s
There is no (42, 99, 36763)-net in base 25, because
- 1 times m-reduction [i] would yield (42, 98, 36763)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 99570 417540 698428 313952 623355 432662 827751 760969 582193 227816 541758 019540 634537 609635 087221 028017 364016 207875 931234 765254 804997 129893 677025 > 2598 [i]