Best Known (7, 7+9, s)-Nets in Base 25
(7, 7+9, 78)-Net over F25 — Constructive and digital
Digital (7, 16, 78)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (3, 12, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (0, 4, 26)-net over F25, using
(7, 7+9, 137)-Net over F25 — Digital
Digital (7, 16, 137)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2516, 137, F25, 9) (dual of [137, 121, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2516, 208, F25, 9) (dual of [208, 192, 10]-code), using
(7, 7+9, 16109)-Net in Base 25 — Upper bound on s
There is no (7, 16, 16110)-net in base 25, because
- 1 times m-reduction [i] would yield (7, 15, 16110)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 931 527310 479147 576001 > 2515 [i]