Best Known (41, 41+20, s)-Nets in Base 4
(41, 41+20, 195)-Net over F4 — Constructive and digital
Digital (41, 61, 195)-net over F4, using
- 41 times duplication [i] based on digital (40, 60, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 20, 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, 20, 65)-net over F64, using
(41, 41+20, 244)-Net over F4 — Digital
Digital (41, 61, 244)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(461, 244, F4, 20) (dual of [244, 183, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(461, 255, F4, 20) (dual of [255, 194, 21]-code), using
(41, 41+20, 7094)-Net in Base 4 — Upper bound on s
There is no (41, 61, 7095)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 5 318187 931445 437255 198717 249880 947570 > 461 [i]