Best Known (37−15, 37, s)-Nets in Base 8
(37−15, 37, 208)-Net over F8 — Constructive and digital
Digital (22, 37, 208)-net over F8, using
- 1 times m-reduction [i] based on digital (22, 38, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 19, 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, 19, 104)-net over F64, using
(37−15, 37, 233)-Net over F8 — Digital
Digital (22, 37, 233)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(837, 233, F8, 15) (dual of [233, 196, 16]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(836, 226, F8, 15) (dual of [226, 190, 16]-code), using
- trace code [i] based on linear OA(6418, 113, F64, 15) (dual of [113, 95, 16]-code), using
- extended algebraic-geometric code AGe(F,97P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- trace code [i] based on linear OA(6418, 113, F64, 15) (dual of [113, 95, 16]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(836, 226, F8, 15) (dual of [226, 190, 16]-code), using
(37−15, 37, 258)-Net in Base 8 — Constructive
(22, 37, 258)-net in base 8, using
- 1 times m-reduction [i] based on (22, 38, 258)-net in base 8, using
- trace code for nets [i] based on (3, 19, 129)-net in base 64, using
- 2 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
- 2 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- trace code for nets [i] based on (3, 19, 129)-net in base 64, using
(37−15, 37, 21291)-Net in Base 8 — Upper bound on s
There is no (22, 37, 21292)-net in base 8, because
- 1 times m-reduction [i] would yield (22, 36, 21292)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 324 595110 937714 422969 860182 732814 > 836 [i]