Best Known (174−20, 174, s)-Nets in Base 3
(174−20, 174, 159435)-Net over F3 — Constructive and digital
Digital (154, 174, 159435)-net over F3, using
- net defined by OOA [i] based on linear OOA(3174, 159435, F3, 20, 20) (dual of [(159435, 20), 3188526, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3174, 1594350, F3, 20) (dual of [1594350, 1594176, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3174, 1594353, F3, 20) (dual of [1594353, 1594179, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3174, 1594353, F3, 20) (dual of [1594353, 1594179, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3174, 1594350, F3, 20) (dual of [1594350, 1594176, 21]-code), using
(174−20, 174, 427294)-Net over F3 — Digital
Digital (154, 174, 427294)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3174, 427294, F3, 3, 20) (dual of [(427294, 3), 1281708, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3174, 531451, F3, 3, 20) (dual of [(531451, 3), 1594179, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3174, 1594353, F3, 20) (dual of [1594353, 1594179, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(19) ⊂ Ce(16) [i] based on
- OOA 3-folding [i] based on linear OA(3174, 1594353, F3, 20) (dual of [1594353, 1594179, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(3174, 531451, F3, 3, 20) (dual of [(531451, 3), 1594179, 21]-NRT-code), using
(174−20, 174, large)-Net in Base 3 — Upper bound on s
There is no (154, 174, large)-net in base 3, because
- 18 times m-reduction [i] would yield (154, 156, large)-net in base 3, but