Best Known (71, 95, s)-Nets in Base 8
(71, 95, 683)-Net over F8 — Constructive and digital
Digital (71, 95, 683)-net over F8, using
- 81 times duplication [i] based on digital (70, 94, 683)-net over F8, using
- net defined by OOA [i] based on linear OOA(894, 683, F8, 24, 24) (dual of [(683, 24), 16298, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(894, 8196, F8, 24) (dual of [8196, 8102, 25]-code), using
- trace code [i] based on linear OA(6447, 4098, F64, 24) (dual of [4098, 4051, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(6447, 4096, F64, 24) (dual of [4096, 4049, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(6445, 4096, F64, 23) (dual of [4096, 4051, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- trace code [i] based on linear OA(6447, 4098, F64, 24) (dual of [4098, 4051, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(894, 8196, F8, 24) (dual of [8196, 8102, 25]-code), using
- net defined by OOA [i] based on linear OOA(894, 683, F8, 24, 24) (dual of [(683, 24), 16298, 25]-NRT-code), using
(71, 95, 772)-Net in Base 8 — Constructive
(71, 95, 772)-net in base 8, using
- 1 times m-reduction [i] based on (71, 96, 772)-net in base 8, using
- (u, u+v)-construction [i] based on
- (16, 28, 258)-net in base 8, using
- trace code for nets [i] based on (2, 14, 129)-net in base 64, using
- base change [i] based on digital (0, 12, 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, 12, 129)-net over F128, using
- trace code for nets [i] based on (2, 14, 129)-net in base 64, using
- (43, 68, 514)-net in base 8, using
- base change [i] based on digital (26, 51, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (26, 52, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 26, 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, 26, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (26, 52, 514)-net over F16, using
- base change [i] based on digital (26, 51, 514)-net over F16, using
- (16, 28, 258)-net in base 8, using
- (u, u+v)-construction [i] based on
(71, 95, 8198)-Net over F8 — Digital
Digital (71, 95, 8198)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(895, 8198, F8, 24) (dual of [8198, 8103, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(894, 8196, F8, 24) (dual of [8196, 8102, 25]-code), using
- trace code [i] based on linear OA(6447, 4098, F64, 24) (dual of [4098, 4051, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(6447, 4096, F64, 24) (dual of [4096, 4049, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(6445, 4096, F64, 23) (dual of [4096, 4051, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- trace code [i] based on linear OA(6447, 4098, F64, 24) (dual of [4098, 4051, 25]-code), using
- linear OA(894, 8197, F8, 23) (dual of [8197, 8103, 24]-code), using Gilbert–Varšamov bound and bm = 894 > Vbs−1(k−1) = 425156 764219 842984 192170 972658 314525 249359 370109 311791 036893 668792 118051 695625 955328 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(894, 8196, F8, 24) (dual of [8196, 8102, 25]-code), using
- construction X with Varšamov bound [i] based on
(71, 95, large)-Net in Base 8 — Upper bound on s
There is no (71, 95, large)-net in base 8, because
- 22 times m-reduction [i] would yield (71, 73, large)-net in base 8, but