Best Known (124−46, 124, s)-Nets in Base 8
(124−46, 124, 354)-Net over F8 — Constructive and digital
Digital (78, 124, 354)-net over F8, using
- 18 times m-reduction [i] based on digital (78, 142, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 71, 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, 71, 177)-net over F64, using
(124−46, 124, 514)-Net in Base 8 — Constructive
(78, 124, 514)-net in base 8, using
- base change [i] based on digital (47, 93, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (47, 94, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 47, 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, 47, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (47, 94, 514)-net over F16, using
(124−46, 124, 798)-Net over F8 — Digital
Digital (78, 124, 798)-net over F8, using
(124−46, 124, 99570)-Net in Base 8 — Upper bound on s
There is no (78, 124, 99571)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 9621 647090 892213 827984 431773 940915 854539 093837 509897 152264 696021 674462 526882 342678 504522 683994 695919 825351 379872 > 8124 [i]