Best Known (25−12, 25, s)-Nets in Base 7
(25−12, 25, 100)-Net over F7 — Constructive and digital
Digital (13, 25, 100)-net over F7, using
- 1 times m-reduction [i] based on digital (13, 26, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 13, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 13, 50)-net over F49, using
(25−12, 25, 1653)-Net in Base 7 — Upper bound on s
There is no (13, 25, 1654)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 1343 668331 957650 803685 > 725 [i]