Best Known (84−10, 84, s)-Nets in Base 8
(84−10, 84, 3355570)-Net over F8 — Constructive and digital
Digital (74, 84, 3355570)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 5, 65)-net over F64, using
- digital (64, 74, 3355440)-net over F8, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- digital (5, 10, 130)-net over F8, using
(84−10, 84, large)-Net over F8 — Digital
Digital (74, 84, large)-net over F8, using
- 83 times duplication [i] based on digital (71, 81, large)-net over F8, using
- t-expansion [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
- t-expansion [i] based on digital (69, 81, large)-net over F8, using
(84−10, 84, large)-Net in Base 8 — Upper bound on s
There is no (74, 84, large)-net in base 8, because
- 8 times m-reduction [i] would yield (74, 76, large)-net in base 8, but