Best Known (96−11, 96, s)-Nets in Base 3
(96−11, 96, 318870)-Net over F3 — Constructive and digital
Digital (85, 96, 318870)-net over F3, using
- net defined by OOA [i] based on linear OOA(396, 318870, F3, 11, 11) (dual of [(318870, 11), 3507474, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(396, 1594351, F3, 11) (dual of [1594351, 1594255, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(396, 1594353, F3, 11) (dual of [1594353, 1594257, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(366, 1594323, F3, 8) (dual of [1594323, 1594257, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(34, 30, F3, 2) (dual of [30, 26, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(396, 1594353, F3, 11) (dual of [1594353, 1594257, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(396, 1594351, F3, 11) (dual of [1594351, 1594255, 12]-code), using
(96−11, 96, 760030)-Net over F3 — Digital
Digital (85, 96, 760030)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(396, 760030, F3, 2, 11) (dual of [(760030, 2), 1519964, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(396, 797176, F3, 2, 11) (dual of [(797176, 2), 1594256, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(396, 1594352, F3, 11) (dual of [1594352, 1594256, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(396, 1594353, F3, 11) (dual of [1594353, 1594257, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(366, 1594323, F3, 8) (dual of [1594323, 1594257, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(34, 30, F3, 2) (dual of [30, 26, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(396, 1594353, F3, 11) (dual of [1594353, 1594257, 12]-code), using
- OOA 2-folding [i] based on linear OA(396, 1594352, F3, 11) (dual of [1594352, 1594256, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(396, 797176, F3, 2, 11) (dual of [(797176, 2), 1594256, 12]-NRT-code), using
(96−11, 96, large)-Net in Base 3 — Upper bound on s
There is no (85, 96, large)-net in base 3, because
- 9 times m-reduction [i] would yield (85, 87, large)-net in base 3, but