Best Known (25−8, 25, s)-Nets in Base 3
(25−8, 25, 84)-Net over F3 — Constructive and digital
Digital (17, 25, 84)-net over F3, using
- 31 times duplication [i] based on digital (16, 24, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 8, 28)-net over F27, using
(25−8, 25, 117)-Net over F3 — Digital
Digital (17, 25, 117)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(325, 117, F3, 8) (dual of [117, 92, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(325, 121, F3, 8) (dual of [121, 96, 9]-code), using
(25−8, 25, 1058)-Net in Base 3 — Upper bound on s
There is no (17, 25, 1059)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 849604 136153 > 325 [i]