Best Known (76, 89, s)-Nets in Base 7
(76, 89, 960801)-Net over F7 — Constructive and digital
Digital (76, 89, 960801)-net over F7, using
- net defined by OOA [i] based on linear OOA(789, 960801, F7, 13, 13) (dual of [(960801, 13), 12490324, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(789, 5764807, F7, 13) (dual of [5764807, 5764718, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(789, 5764809, F7, 13) (dual of [5764809, 5764720, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(789, 5764801, F7, 13) (dual of [5764801, 5764712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(789, 5764809, F7, 13) (dual of [5764809, 5764720, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(789, 5764807, F7, 13) (dual of [5764807, 5764718, 14]-code), using
(76, 89, 4716791)-Net over F7 — Digital
Digital (76, 89, 4716791)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(789, 4716791, F7, 13) (dual of [4716791, 4716702, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(789, 5764801, F7, 13) (dual of [5764801, 5764712, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(789, 5764801, F7, 13) (dual of [5764801, 5764712, 14]-code), using
(76, 89, large)-Net in Base 7 — Upper bound on s
There is no (76, 89, large)-net in base 7, because
- 11 times m-reduction [i] would yield (76, 78, large)-net in base 7, but