Best Known (23, 36, s)-Nets in Base 8
(23, 36, 256)-Net over F8 — Constructive and digital
Digital (23, 36, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 18, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(23, 36, 514)-Net in Base 8 — Constructive
(23, 36, 514)-net in base 8, using
- base change [i] based on digital (14, 27, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (14, 28, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 14, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 14, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (14, 28, 514)-net over F16, using
(23, 36, 518)-Net over F8 — Digital
Digital (23, 36, 518)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(836, 518, F8, 13) (dual of [518, 482, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(836, 521, F8, 13) (dual of [521, 485, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(834, 512, F8, 13) (dual of [512, 478, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(825, 512, F8, 10) (dual of [512, 487, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(836, 521, F8, 13) (dual of [521, 485, 14]-code), using
(23, 36, 79273)-Net in Base 8 — Upper bound on s
There is no (23, 36, 79274)-net in base 8, because
- 1 times m-reduction [i] would yield (23, 35, 79274)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 40 564929 384392 450740 588455 037924 > 835 [i]