Best Known (9, 15, s)-Nets in Base 8
(9, 15, 160)-Net over F8 — Constructive and digital
Digital (9, 15, 160)-net over F8, using
- 1 times m-reduction [i] based on digital (9, 16, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 8, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 8, 80)-net over F64, using
(9, 15, 203)-Net over F8 — Digital
Digital (9, 15, 203)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(815, 203, F8, 6) (dual of [203, 188, 7]-code), using
- 40 step Varšamov–Edel lengthening with (ri) = (1, 39 times 0) [i] based on linear OA(814, 162, F8, 6) (dual of [162, 148, 7]-code), using
- trace code [i] based on linear OA(647, 81, F64, 6) (dual of [81, 74, 7]-code), using
- extended algebraic-geometric code AGe(F,74P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
- trace code [i] based on linear OA(647, 81, F64, 6) (dual of [81, 74, 7]-code), using
- 40 step Varšamov–Edel lengthening with (ri) = (1, 39 times 0) [i] based on linear OA(814, 162, F8, 6) (dual of [162, 148, 7]-code), using
(9, 15, 258)-Net in Base 8 — Constructive
(9, 15, 258)-net in base 8, using
- 81 times duplication [i] based on (8, 14, 258)-net in base 8, using
- trace code for nets [i] based on (1, 7, 129)-net in base 64, using
- base change [i] based on digital (0, 6, 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, 6, 129)-net over F128, using
- trace code for nets [i] based on (1, 7, 129)-net in base 64, using
(9, 15, 8504)-Net in Base 8 — Upper bound on s
There is no (9, 15, 8505)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 35 187193 849816 > 815 [i]