Best Known (78, 88, s)-Nets in Base 8
(78, 88, 3359472)-Net over F8 — Constructive and digital
Digital (78, 88, 3359472)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (9, 14, 4032)-net over F8, using
- net defined by OOA [i] based on linear OOA(814, 4032, F8, 5, 5) (dual of [(4032, 5), 20146, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(814, 8065, F8, 5) (dual of [8065, 8051, 6]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(814, 8065, F8, 5) (dual of [8065, 8051, 6]-code), using
- net defined by OOA [i] based on linear OOA(814, 4032, F8, 5, 5) (dual of [(4032, 5), 20146, 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 (9, 14, 4032)-net over F8, using
(78, 88, large)-Net over F8 — Digital
Digital (78, 88, large)-net over F8, using
- t-expansion [i] based on digital (76, 88, large)-net over F8, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on digital (76, 89, large)-net over F8, using
(78, 88, large)-Net in Base 8 — Upper bound on s
There is no (78, 88, large)-net in base 8, because
- 8 times m-reduction [i] would yield (78, 80, large)-net in base 8, but