Best Known (59, 59+34, s)-Nets in Base 8
(59, 59+34, 354)-Net over F8 — Constructive and digital
Digital (59, 93, 354)-net over F8, using
- 11 times m-reduction [i] based on digital (59, 104, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 52, 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, 52, 177)-net over F64, using
(59, 59+34, 514)-Net in Base 8 — Constructive
(59, 93, 514)-net in base 8, using
- 1 times m-reduction [i] based on (59, 94, 514)-net in base 8, using
- trace code for nets [i] based on (12, 47, 257)-net in base 64, using
- 1 times m-reduction [i] based on (12, 48, 257)-net in base 64, using
- base change [i] based on digital (0, 36, 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, 36, 257)-net over F256, using
- 1 times m-reduction [i] based on (12, 48, 257)-net in base 64, using
- trace code for nets [i] based on (12, 47, 257)-net in base 64, using
(59, 59+34, 676)-Net over F8 — Digital
Digital (59, 93, 676)-net over F8, using
(59, 59+34, 89377)-Net in Base 8 — Upper bound on s
There is no (59, 93, 89378)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 971360 136921 302704 795738 430211 505905 706890 743130 527564 630656 680506 557089 322190 648074 > 893 [i]