Best Known (99−11, 99, s)-Nets in Base 8
(99−11, 99, 3359545)-Net over F8 — Constructive and digital
Digital (88, 99, 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 (71, 82, 3355440)-net over F8, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- digital (12, 17, 4105)-net over F8, using
(99−11, 99, 3363568)-Net in Base 8 — Constructive
(88, 99, 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 (71, 82, 3355440)-net over F8, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- (12, 17, 8128)-net in base 8, using
(99−11, 99, large)-Net over F8 — Digital
Digital (88, 99, large)-net over F8, using
- 82 times duplication [i] based on digital (86, 97, large)-net over F8, using
- t-expansion [i] based on digital (83, 97, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
- t-expansion [i] based on digital (83, 97, large)-net over F8, using
(99−11, 99, large)-Net in Base 8 — Upper bound on s
There is no (88, 99, large)-net in base 8, because
- 9 times m-reduction [i] would yield (88, 90, large)-net in base 8, but