Best Known (31, 53, s)-Nets in Base 8
(31, 53, 208)-Net over F8 — Constructive and digital
Digital (31, 53, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (31, 56, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 28, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 28, 104)-net over F64, using
(31, 53, 258)-Net in Base 8 — Constructive
(31, 53, 258)-net in base 8, using
- 1 times m-reduction [i] based on (31, 54, 258)-net in base 8, using
- trace code for nets [i] based on (4, 27, 129)-net in base 64, using
- 1 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- 1 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- trace code for nets [i] based on (4, 27, 129)-net in base 64, using
(31, 53, 258)-Net over F8 — Digital
Digital (31, 53, 258)-net over F8, using
- 1 times m-reduction [i] based on digital (31, 54, 258)-net over F8, using
- trace code for nets [i] based on digital (4, 27, 129)-net over F64, using
- net from sequence [i] based on digital (4, 128)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- net from sequence [i] based on digital (4, 128)-sequence over F64, using
- trace code for nets [i] based on digital (4, 27, 129)-net over F64, using
(31, 53, 15739)-Net in Base 8 — Upper bound on s
There is no (31, 53, 15740)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 731086 115024 285841 909595 142277 477346 746712 179557 > 853 [i]