Best Known (86−32, 86, s)-Nets in Base 8
(86−32, 86, 354)-Net over F8 — Constructive and digital
Digital (54, 86, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (54, 94, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 47, 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, 47, 177)-net over F64, using
(86−32, 86, 514)-Net in Base 8 — Constructive
(54, 86, 514)-net in base 8, using
- trace code for nets [i] based on (11, 43, 257)-net in base 64, using
- 1 times m-reduction [i] based on (11, 44, 257)-net in base 64, using
- base change [i] based on digital (0, 33, 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
- base change [i] based on digital (0, 33, 257)-net over F256, using
- 1 times m-reduction [i] based on (11, 44, 257)-net in base 64, using
(86−32, 86, 583)-Net over F8 — Digital
Digital (54, 86, 583)-net over F8, using
(86−32, 86, 69420)-Net in Base 8 — Upper bound on s
There is no (54, 86, 69421)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 463214 646092 996821 481778 718386 522952 566931 609925 568635 580819 548793 672978 210698 > 886 [i]