Best Known (25, 25+12, s)-Nets in Base 4
(25, 25+12, 195)-Net over F4 — Constructive and digital
Digital (25, 37, 195)-net over F4, using
- 41 times duplication [i] based on digital (24, 36, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 12, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 12, 65)-net over F64, using
(25, 25+12, 215)-Net over F4 — Digital
Digital (25, 37, 215)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(437, 215, F4, 12) (dual of [215, 178, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(437, 255, F4, 12) (dual of [255, 218, 13]-code), using
(25, 25+12, 5145)-Net in Base 4 — Upper bound on s
There is no (25, 37, 5146)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 18901 252467 851950 815004 > 437 [i]