Best Known (15−7, 15, s)-Nets in Base 5
(15−7, 15, 52)-Net over F5 — Constructive and digital
Digital (8, 15, 52)-net over F5, using
- 1 times m-reduction [i] based on digital (8, 16, 52)-net over F5, using
- trace code for nets [i] based on digital (0, 8, 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
- trace code for nets [i] based on digital (0, 8, 26)-net over F25, using
(15−7, 15, 57)-Net over F5 — Digital
Digital (8, 15, 57)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(515, 57, F5, 7) (dual of [57, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(515, 62, F5, 7) (dual of [62, 47, 8]-code), using
(15−7, 15, 828)-Net in Base 5 — Upper bound on s
There is no (8, 15, 829)-net in base 5, because
- 1 times m-reduction [i] would yield (8, 14, 829)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 6115 576109 > 514 [i]