Best Known (25−12, 25, s)-Nets in Base 5
(25−12, 25, 52)-Net over F5 — Constructive and digital
Digital (13, 25, 52)-net over F5, using
- 1 times m-reduction [i] based on digital (13, 26, 52)-net over F5, using
- trace code for nets [i] based on digital (0, 13, 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, 13, 26)-net over F25, using
(25−12, 25, 607)-Net in Base 5 — Upper bound on s
There is no (13, 25, 608)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 298877 575709 933057 > 525 [i]