Best Known (77, 77+13, s)-Nets in Base 8
(77, 77+13, 1398100)-Net over F8 — Constructive and digital
Digital (77, 90, 1398100)-net over F8, using
- 81 times duplication [i] based on digital (76, 89, 1398100)-net over F8, using
- net defined by OOA [i] based on linear OOA(889, 1398100, F8, 13, 13) (dual of [(1398100, 13), 18175211, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(889, 8388601, F8, 13) (dual of [8388601, 8388512, 14]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(889, large, F8, 13) (dual of [large, large−89, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(889, 8388601, F8, 13) (dual of [8388601, 8388512, 14]-code), using
- net defined by OOA [i] based on linear OOA(889, 1398100, F8, 13, 13) (dual of [(1398100, 13), 18175211, 14]-NRT-code), using
(77, 77+13, large)-Net over F8 — Digital
Digital (77, 90, large)-net over F8, using
- 81 times duplication [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
(77, 77+13, large)-Net in Base 8 — Upper bound on s
There is no (77, 90, large)-net in base 8, because
- 11 times m-reduction [i] would yield (77, 79, large)-net in base 8, but