Best Known (75, 87, s)-Nets in Base 8
(75, 87, 1398109)-Net over F8 — Constructive and digital
Digital (75, 87, 1398109)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (69, 81, 1398100)-net over F8, using
- net defined by OOA [i] based on linear OOA(881, 1398100, F8, 12, 12) (dual of [(1398100, 12), 16777119, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(881, 8388600, F8, 12) (dual of [8388600, 8388519, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(881, 8388600, F8, 12) (dual of [8388600, 8388519, 13]-code), using
- net defined by OOA [i] based on linear OOA(881, 1398100, F8, 12, 12) (dual of [(1398100, 12), 16777119, 13]-NRT-code), using
- digital (0, 6, 9)-net over F8, using
(75, 87, large)-Net over F8 — Digital
Digital (75, 87, large)-net over F8, using
- 86 times duplication [i] based on digital (69, 81, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
(75, 87, large)-Net in Base 8 — Upper bound on s
There is no (75, 87, large)-net in base 8, because
- 10 times m-reduction [i] would yield (75, 77, large)-net in base 8, but