Best Known (168, 168+56, s)-Nets in Base 4
(168, 168+56, 1028)-Net over F4 — Constructive and digital
Digital (168, 224, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 56, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(168, 168+56, 2041)-Net over F4 — Digital
Digital (168, 224, 2041)-net over F4, using
(168, 168+56, 246787)-Net in Base 4 — Upper bound on s
There is no (168, 224, 246788)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 726 862702 538758 706984 872161 248465 226654 043687 183398 153721 213714 891026 919276 172627 589377 231053 963409 204555 946781 305059 623879 452184 472320 > 4224 [i]