Best Known (76, 76+13, s)-Nets in Base 9
(76, 76+13, 1398100)-Net over F9 — Constructive and digital
Digital (76, 89, 1398100)-net over F9, using
- net defined by OOA [i] based on linear OOA(989, 1398100, F9, 13, 13) (dual of [(1398100, 13), 18175211, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(989, 8388601, F9, 13) (dual of [8388601, 8388512, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(989, large, F9, 13) (dual of [large, large−89, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(989, large, F9, 13) (dual of [large, large−89, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(989, 8388601, F9, 13) (dual of [8388601, 8388512, 14]-code), using
(76, 76+13, large)-Net over F9 — Digital
Digital (76, 89, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(989, large, F9, 13) (dual of [large, large−89, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
(76, 76+13, large)-Net in Base 9 — Upper bound on s
There is no (76, 89, large)-net in base 9, because
- 11 times m-reduction [i] would yield (76, 78, large)-net in base 9, but