Best Known (25−12, 25, s)-Nets in Base 9
(25−12, 25, 164)-Net over F9 — Constructive and digital
Digital (13, 25, 164)-net over F9, using
- 1 times m-reduction [i] based on digital (13, 26, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 13, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 13, 82)-net over F81, using
(25−12, 25, 3537)-Net in Base 9 — Upper bound on s
There is no (13, 25, 3538)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 718035 984557 354529 132705 > 925 [i]