Best Known (33−13, 33, s)-Nets in Base 8
(33−13, 33, 208)-Net over F8 — Constructive and digital
Digital (20, 33, 208)-net over F8, using
- 1 times m-reduction [i] based on digital (20, 34, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 17, 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, 17, 104)-net over F64, using
(33−13, 33, 244)-Net over F8 — Digital
Digital (20, 33, 244)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(833, 244, F8, 13) (dual of [244, 211, 14]-code), using
- 17 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0) [i] based on linear OA(832, 226, F8, 13) (dual of [226, 194, 14]-code), using
- trace code [i] based on linear OA(6416, 113, F64, 13) (dual of [113, 97, 14]-code), using
- extended algebraic-geometric code AGe(F,99P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- trace code [i] based on linear OA(6416, 113, F64, 13) (dual of [113, 97, 14]-code), using
- 17 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0) [i] based on linear OA(832, 226, F8, 13) (dual of [226, 194, 14]-code), using
(33−13, 33, 258)-Net in Base 8 — Constructive
(20, 33, 258)-net in base 8, using
- 1 times m-reduction [i] based on (20, 34, 258)-net in base 8, using
- trace code for nets [i] based on (3, 17, 129)-net in base 64, using
- 4 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- base change [i] based on digital (0, 18, 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, 18, 129)-net over F128, using
- 4 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- trace code for nets [i] based on (3, 17, 129)-net in base 64, using
(33−13, 33, 28025)-Net in Base 8 — Upper bound on s
There is no (20, 33, 28026)-net in base 8, because
- 1 times m-reduction [i] would yield (20, 32, 28026)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 79238 191409 064738 293716 545724 > 832 [i]