Best Known (80, 80+15, s)-Nets in Base 9
(80, 80+15, 683284)-Net over F9 — Constructive and digital
Digital (80, 95, 683284)-net over F9, using
- net defined by OOA [i] based on linear OOA(995, 683284, F9, 15, 15) (dual of [(683284, 15), 10249165, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(995, 4782989, F9, 15) (dual of [4782989, 4782894, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(995, 4782993, F9, 15) (dual of [4782993, 4782898, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(14) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(995, 4782993, F9, 15) (dual of [4782993, 4782898, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(995, 4782989, F9, 15) (dual of [4782989, 4782894, 16]-code), using
(80, 80+15, 4782993)-Net over F9 — Digital
Digital (80, 95, 4782993)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(995, 4782993, F9, 15) (dual of [4782993, 4782898, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(14) ⊂ Ce(11) [i] based on
(80, 80+15, large)-Net in Base 9 — Upper bound on s
There is no (80, 95, large)-net in base 9, because
- 13 times m-reduction [i] would yield (80, 82, large)-net in base 9, but