Best Known (51, 51+30, s)-Nets in Base 8
(51, 51+30, 354)-Net over F8 — Constructive and digital
Digital (51, 81, 354)-net over F8, using
- 7 times m-reduction [i] based on digital (51, 88, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 44, 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, 44, 177)-net over F64, using
(51, 51+30, 514)-Net in Base 8 — Constructive
(51, 81, 514)-net in base 8, using
- 81 times duplication [i] based on (50, 80, 514)-net in base 8, using
- base change [i] based on digital (30, 60, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 30, 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
- trace code for nets [i] based on digital (0, 30, 257)-net over F256, using
- base change [i] based on digital (30, 60, 514)-net over F16, using
(51, 51+30, 570)-Net over F8 — Digital
Digital (51, 81, 570)-net over F8, using
(51, 51+30, 69071)-Net in Base 8 — Upper bound on s
There is no (51, 81, 69072)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 14 137208 390207 699369 377626 830180 769497 371339 150098 160131 127417 581504 284551 > 881 [i]