Best Known (88−14, 88, s)-Nets in Base 8
(88−14, 88, 299596)-Net over F8 — Constructive and digital
Digital (74, 88, 299596)-net over F8, using
- net defined by OOA [i] based on linear OOA(888, 299596, F8, 14, 14) (dual of [(299596, 14), 4194256, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(888, 2097172, F8, 14) (dual of [2097172, 2097084, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(888, 2097176, F8, 14) (dual of [2097176, 2097088, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(888, 2097176, F8, 14) (dual of [2097176, 2097088, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(888, 2097172, F8, 14) (dual of [2097172, 2097084, 15]-code), using
(88−14, 88, 2097176)-Net over F8 — Digital
Digital (74, 88, 2097176)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(888, 2097176, F8, 14) (dual of [2097176, 2097088, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
(88−14, 88, large)-Net in Base 8 — Upper bound on s
There is no (74, 88, large)-net in base 8, because
- 12 times m-reduction [i] would yield (74, 76, large)-net in base 8, but