Best Known (12−7, 12, s)-Nets in Base 25
(12−7, 12, 78)-Net over F25 — Constructive and digital
Digital (5, 12, 78)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 26)-net over F25, using
- digital (0, 3, 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 (0, 7, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25 (see above)
(12−7, 12, 89)-Net over F25 — Digital
Digital (5, 12, 89)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2512, 89, F25, 7) (dual of [89, 77, 8]-code), using
(12−7, 12, 10113)-Net in Base 25 — Upper bound on s
There is no (5, 12, 10114)-net in base 25, because
- 1 times m-reduction [i] would yield (5, 11, 10114)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2384 493983 406289 > 2511 [i]