Best Known (39−16, 39, s)-Nets in Base 8
(39−16, 39, 208)-Net over F8 — Constructive and digital
Digital (23, 39, 208)-net over F8, using
- 1 times m-reduction [i] based on digital (23, 40, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 20, 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, 20, 104)-net over F64, using
(39−16, 39, 230)-Net over F8 — Digital
Digital (23, 39, 230)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(839, 230, F8, 16) (dual of [230, 191, 17]-code), using
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(838, 226, F8, 16) (dual of [226, 188, 17]-code), using
- trace code [i] based on linear OA(6419, 113, F64, 16) (dual of [113, 94, 17]-code), using
- extended algebraic-geometric code AGe(F,96P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- trace code [i] based on linear OA(6419, 113, F64, 16) (dual of [113, 94, 17]-code), using
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(838, 226, F8, 16) (dual of [226, 188, 17]-code), using
(39−16, 39, 258)-Net in Base 8 — Constructive
(23, 39, 258)-net in base 8, using
- 1 times m-reduction [i] based on (23, 40, 258)-net in base 8, using
- trace code for nets [i] based on (3, 20, 129)-net in base 64, using
- 1 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
- 1 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- trace code for nets [i] based on (3, 20, 129)-net in base 64, using
(39−16, 39, 13583)-Net in Base 8 — Upper bound on s
There is no (23, 39, 13584)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 166215 812560 470815 940799 866719 104195 > 839 [i]