Best Known (70, 112, s)-Nets in Base 8
(70, 112, 354)-Net over F8 — Constructive and digital
Digital (70, 112, 354)-net over F8, using
- 14 times m-reduction [i] based on digital (70, 126, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 63, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 63, 177)-net over F64, using
(70, 112, 514)-Net in Base 8 — Constructive
(70, 112, 514)-net in base 8, using
- base change [i] based on digital (42, 84, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 42, 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, 42, 257)-net over F256, using
(70, 112, 696)-Net over F8 — Digital
Digital (70, 112, 696)-net over F8, using
(70, 112, 81246)-Net in Base 8 — Upper bound on s
There is no (70, 112, 81247)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 139999 999399 178693 956524 160993 135424 206015 913551 523514 964549 497049 798140 829347 333879 246911 834103 905490 > 8112 [i]