Best Known (78−30, 78, s)-Nets in Base 8
(78−30, 78, 354)-Net over F8 — Constructive and digital
Digital (48, 78, 354)-net over F8, using
- 4 times m-reduction [i] based on digital (48, 82, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 41, 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, 41, 177)-net over F64, using
(78−30, 78, 384)-Net in Base 8 — Constructive
(48, 78, 384)-net in base 8, using
- trace code for nets [i] based on (9, 39, 192)-net in base 64, using
- 3 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- 3 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
(78−30, 78, 462)-Net over F8 — Digital
Digital (48, 78, 462)-net over F8, using
(78−30, 78, 45566)-Net in Base 8 — Upper bound on s
There is no (48, 78, 45567)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 27607 966676 698625 463489 020387 590173 583136 444658 279284 730827 077389 215640 > 878 [i]