Best Known (74, 88, s)-Nets in Base 9
(74, 88, 683284)-Net over F9 — Constructive and digital
Digital (74, 88, 683284)-net over F9, using
- net defined by OOA [i] based on linear OOA(988, 683284, F9, 14, 14) (dual of [(683284, 14), 9565888, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(988, 4782988, F9, 14) (dual of [4782988, 4782900, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(988, 4782993, F9, 14) (dual of [4782993, 4782905, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(964, 4782969, F9, 11) (dual of [4782969, 4782905, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(93, 24, F9, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(988, 4782993, F9, 14) (dual of [4782993, 4782905, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(988, 4782988, F9, 14) (dual of [4782988, 4782900, 15]-code), using
(74, 88, 4782993)-Net over F9 — Digital
Digital (74, 88, 4782993)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(988, 4782993, F9, 14) (dual of [4782993, 4782905, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(964, 4782969, F9, 11) (dual of [4782969, 4782905, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(93, 24, F9, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
(74, 88, large)-Net in Base 9 — Upper bound on s
There is no (74, 88, large)-net in base 9, because
- 12 times m-reduction [i] would yield (74, 76, large)-net in base 9, but