Best Known (81, 125, s)-Nets in Base 8
(81, 125, 368)-Net over F8 — Constructive and digital
Digital (81, 125, 368)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 23, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- digital (58, 102, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 51, 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, 51, 177)-net over F64, using
- digital (1, 23, 14)-net over F8, using
(81, 125, 576)-Net in Base 8 — Constructive
(81, 125, 576)-net in base 8, using
- 1 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
(81, 125, 1039)-Net over F8 — Digital
Digital (81, 125, 1039)-net over F8, using
(81, 125, 174950)-Net in Base 8 — Upper bound on s
There is no (81, 125, 174951)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 76965 616283 887285 566314 934310 126607 994880 985957 687559 373281 752197 152414 003776 326727 291615 752915 735242 550157 936474 > 8125 [i]