Best Known (84−32, 84, s)-Nets in Base 8
(84−32, 84, 354)-Net over F8 — Constructive and digital
Digital (52, 84, 354)-net over F8, using
- 6 times m-reduction [i] based on digital (52, 90, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 45, 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, 45, 177)-net over F64, using
(84−32, 84, 384)-Net in Base 8 — Constructive
(52, 84, 384)-net in base 8, using
- t-expansion [i] based on (51, 84, 384)-net in base 8, using
- trace code for nets [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
- trace code for nets [i] based on (9, 42, 192)-net in base 64, using
(84−32, 84, 512)-Net over F8 — Digital
Digital (52, 84, 512)-net over F8, using
(84−32, 84, 53528)-Net in Base 8 — Upper bound on s
There is no (52, 84, 53529)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 7238 444426 643139 988693 807785 933431 531534 230461 456633 437213 016096 220816 410623 > 884 [i]