Best Known (21, 21+14, s)-Nets in Base 8
(21, 21+14, 208)-Net over F8 — Constructive and digital
Digital (21, 35, 208)-net over F8, using
- 1 times m-reduction [i] based on digital (21, 36, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 18, 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, 18, 104)-net over F64, using
(21, 21+14, 237)-Net over F8 — Digital
Digital (21, 35, 237)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(835, 237, F8, 14) (dual of [237, 202, 15]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(834, 226, F8, 14) (dual of [226, 192, 15]-code), using
- trace code [i] based on linear OA(6417, 113, F64, 14) (dual of [113, 96, 15]-code), using
- extended algebraic-geometric code AGe(F,98P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- trace code [i] based on linear OA(6417, 113, F64, 14) (dual of [113, 96, 15]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(834, 226, F8, 14) (dual of [226, 192, 15]-code), using
(21, 21+14, 258)-Net in Base 8 — Constructive
(21, 35, 258)-net in base 8, using
- 1 times m-reduction [i] based on (21, 36, 258)-net in base 8, using
- trace code for nets [i] based on (3, 18, 129)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- trace code for nets [i] based on (3, 18, 129)-net in base 64, using
(21, 21+14, 15818)-Net in Base 8 — Upper bound on s
There is no (21, 35, 15819)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 40 576770 097366 118308 076697 652088 > 835 [i]