Best Known (68, 90, s)-Nets in Base 8
(68, 90, 746)-Net over F8 — Constructive and digital
Digital (68, 90, 746)-net over F8, using
- net defined by OOA [i] based on linear OOA(890, 746, F8, 22, 22) (dual of [(746, 22), 16322, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(890, 8206, F8, 22) (dual of [8206, 8116, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(890, 8208, F8, 22) (dual of [8208, 8118, 23]-code), using
- trace code [i] based on linear OA(6445, 4104, F64, 22) (dual of [4104, 4059, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- trace code [i] based on linear OA(6445, 4104, F64, 22) (dual of [4104, 4059, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(890, 8208, F8, 22) (dual of [8208, 8118, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(890, 8206, F8, 22) (dual of [8206, 8116, 23]-code), using
(68, 90, 1028)-Net in Base 8 — Constructive
(68, 90, 1028)-net in base 8, using
- 82 times duplication [i] based on (66, 88, 1028)-net in base 8, using
- base change [i] based on digital (44, 66, 1028)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (11, 22, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 11, 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, 11, 257)-net over F256, using
- digital (22, 44, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 22, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 22, 257)-net over F256, using
- digital (11, 22, 514)-net over F16, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (44, 66, 1028)-net over F16, using
(68, 90, 9210)-Net over F8 — Digital
Digital (68, 90, 9210)-net over F8, using
(68, 90, large)-Net in Base 8 — Upper bound on s
There is no (68, 90, large)-net in base 8, because
- 20 times m-reduction [i] would yield (68, 70, large)-net in base 8, but