Best Known (75, 99, s)-Nets in Base 8
(75, 99, 684)-Net over F8 — Constructive and digital
Digital (75, 99, 684)-net over F8, using
- 81 times duplication [i] based on digital (74, 98, 684)-net over F8, using
- net defined by OOA [i] based on linear OOA(898, 684, F8, 24, 24) (dual of [(684, 24), 16318, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(898, 8208, F8, 24) (dual of [8208, 8110, 25]-code), using
- trace code [i] based on linear OA(6449, 4104, F64, 24) (dual of [4104, 4055, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [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(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(23) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(6449, 4104, F64, 24) (dual of [4104, 4055, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(898, 8208, F8, 24) (dual of [8208, 8110, 25]-code), using
- net defined by OOA [i] based on linear OOA(898, 684, F8, 24, 24) (dual of [(684, 24), 16318, 25]-NRT-code), using
(75, 99, 1028)-Net in Base 8 — Constructive
(75, 99, 1028)-net in base 8, using
- 1 times m-reduction [i] based on (75, 100, 1028)-net in base 8, using
- base change [i] based on digital (50, 75, 1028)-net over F16, using
- 161 times duplication [i] based on digital (49, 74, 1028)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (12, 24, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 12, 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, 12, 257)-net over F256, using
- digital (25, 50, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 25, 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, 25, 257)-net over F256, using
- digital (12, 24, 514)-net over F16, using
- (u, u+v)-construction [i] based on
- 161 times duplication [i] based on digital (49, 74, 1028)-net over F16, using
- base change [i] based on digital (50, 75, 1028)-net over F16, using
(75, 99, 10400)-Net over F8 — Digital
Digital (75, 99, 10400)-net over F8, using
(75, 99, large)-Net in Base 8 — Upper bound on s
There is no (75, 99, large)-net in base 8, because
- 22 times m-reduction [i] would yield (75, 77, large)-net in base 8, but