Best Known (84, 95, s)-Nets in Base 8
(84, 95, 3357456)-Net over F8 — Constructive and digital
Digital (84, 95, 3357456)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 2016)-net over F8, using
- net defined by OOA [i] based on linear OOA(813, 2016, F8, 5, 5) (dual of [(2016, 5), 10067, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(813, 4033, F8, 5) (dual of [4033, 4020, 6]-code), using
- net defined by OOA [i] based on linear OOA(813, 2016, F8, 5, 5) (dual of [(2016, 5), 10067, 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 (8, 13, 2016)-net over F8, using
(84, 95, large)-Net over F8 — Digital
Digital (84, 95, large)-net over F8, using
- t-expansion [i] based on digital (83, 95, large)-net over F8, using
- 2 times m-reduction [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
- 2 times m-reduction [i] based on digital (83, 97, large)-net over F8, using
(84, 95, large)-Net in Base 8 — Upper bound on s
There is no (84, 95, large)-net in base 8, because
- 9 times m-reduction [i] would yield (84, 86, large)-net in base 8, but