Best Known (58−24, 58, s)-Nets in Base 8
(58−24, 58, 256)-Net over F8 — Constructive and digital
Digital (34, 58, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 29, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(58−24, 58, 258)-Net in Base 8 — Constructive
(34, 58, 258)-net in base 8, using
- 82 times duplication [i] based on (32, 56, 258)-net in base 8, using
- trace code for nets [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
- trace code for nets [i] based on (4, 28, 129)-net in base 64, using
(58−24, 58, 271)-Net over F8 — Digital
Digital (34, 58, 271)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(858, 271, F8, 24) (dual of [271, 213, 25]-code), using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 8 times 0) [i] based on linear OA(856, 258, F8, 24) (dual of [258, 202, 25]-code), using
- trace code [i] based on linear OA(6428, 129, F64, 24) (dual of [129, 101, 25]-code), using
- extended algebraic-geometric code AGe(F,104P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6428, 129, F64, 24) (dual of [129, 101, 25]-code), using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 8 times 0) [i] based on linear OA(856, 258, F8, 24) (dual of [258, 202, 25]-code), using
(58−24, 58, 17499)-Net in Base 8 — Upper bound on s
There is no (34, 58, 17500)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 23957 627126 967232 722106 999310 118655 788800 438825 967876 > 858 [i]