Best Known (19, 19+25, s)-Nets in Base 25
(19, 19+25, 148)-Net over F25 — Constructive and digital
Digital (19, 44, 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
(19, 19+25, 162)-Net over F25 — Digital
Digital (19, 44, 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
(19, 19+25, 22507)-Net in Base 25 — Upper bound on s
There is no (19, 44, 22508)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 43, 22508)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 293093 077618 616129 057912 013387 275786 087084 918555 132009 066625 > 2543 [i]