Best Known (233−58, 233, s)-Nets in Base 4
(233−58, 233, 1028)-Net over F4 — Constructive and digital
Digital (175, 233, 1028)-net over F4, using
- 41 times duplication [i] based on digital (174, 232, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 58, 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
- trace code for nets [i] based on digital (0, 58, 257)-net over F256, using
(233−58, 233, 2156)-Net over F4 — Digital
Digital (175, 233, 2156)-net over F4, using
(233−58, 233, 267425)-Net in Base 4 — Upper bound on s
There is no (175, 233, 267426)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 190 544885 580554 594318 487687 975687 684828 753217 217666 964537 598765 300344 844101 470125 254265 536248 934619 534374 890983 068442 280813 433756 541806 014920 > 4233 [i]