Best Known (81, 91, s)-Nets in Base 8
(81, 91, 3359545)-Net over F8 — Constructive and digital
Digital (81, 91, 3359545)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (12, 17, 4105)-net over F8, using
- net defined by OOA [i] based on linear OOA(817, 4105, F8, 6, 5) (dual of [(4105, 6), 24613, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(817, 4106, F8, 2, 5) (dual of [(4106, 2), 8195, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- Hamming code H(3,8) [i]
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- linear OOA(814, 4033, F8, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- trace code [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- OOA 2-folding [i] based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(817, 4106, F8, 2, 5) (dual of [(4106, 2), 8195, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(817, 4105, F8, 6, 5) (dual of [(4105, 6), 24613, 6]-NRT-code), 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 (12, 17, 4105)-net over F8, using
(81, 91, 3363568)-Net in Base 8 — Constructive
(81, 91, 3363568)-net in base 8, using
- (u, u+v)-construction [i] based on
- (12, 17, 8128)-net in base 8, using
- net defined by OOA [i] based on OOA(817, 8128, S8, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(817, 16257, S8, 5), using
- discarding parts of the base [i] based on linear OA(1287, 16257, F128, 5) (dual of [16257, 16250, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(817, 16257, S8, 5), using
- net defined by OOA [i] based on OOA(817, 8128, S8, 5, 5), 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
- (12, 17, 8128)-net in base 8, using
(81, 91, large)-Net over F8 — Digital
Digital (81, 91, large)-net over F8, using
- 82 times duplication [i] based on digital (79, 89, large)-net over F8, using
- t-expansion [i] based on digital (76, 89, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(889, large, F8, 13) (dual of [large, large−89, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(889, large, F8, 13) (dual of [large, large−89, 14]-code), using
- t-expansion [i] based on digital (76, 89, large)-net over F8, using
(81, 91, large)-Net in Base 8 — Upper bound on s
There is no (81, 91, large)-net in base 8, because
- 8 times m-reduction [i] would yield (81, 83, large)-net in base 8, but