Best Known (66−47, 66, s)-Nets in Base 25
(66−47, 66, 148)-Net over F25 — Constructive and digital
Digital (19, 66, 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
(66−47, 66, 162)-Net over F25 — Digital
Digital (19, 66, 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
(66−47, 66, 3495)-Net in Base 25 — Upper bound on s
There is no (19, 66, 3496)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 65, 3496)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 7 389059 835359 798223 297145 348795 432208 233633 626185 694982 338726 579672 213266 161303 052543 087425 > 2565 [i]