Best Known (132, 158, s)-Nets in Base 3
(132, 158, 1515)-Net over F3 — Constructive and digital
Digital (132, 158, 1515)-net over F3, using
- 31 times duplication [i] based on digital (131, 157, 1515)-net over F3, using
- net defined by OOA [i] based on linear OOA(3157, 1515, F3, 26, 26) (dual of [(1515, 26), 39233, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3157, 19695, F3, 26) (dual of [19695, 19538, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3157, 19696, F3, 26) (dual of [19696, 19539, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3157, 19696, F3, 26) (dual of [19696, 19539, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3157, 19695, F3, 26) (dual of [19695, 19538, 27]-code), using
- net defined by OOA [i] based on linear OOA(3157, 1515, F3, 26, 26) (dual of [(1515, 26), 39233, 27]-NRT-code), using
(132, 158, 8098)-Net over F3 — Digital
Digital (132, 158, 8098)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3158, 8098, F3, 2, 26) (dual of [(8098, 2), 16038, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3158, 9852, F3, 2, 26) (dual of [(9852, 2), 19546, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3158, 19704, F3, 26) (dual of [19704, 19546, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3158, 19705, F3, 26) (dual of [19705, 19547, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(34, 22, F3, 2) (dual of [22, 18, 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(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3158, 19705, F3, 26) (dual of [19705, 19547, 27]-code), using
- OOA 2-folding [i] based on linear OA(3158, 19704, F3, 26) (dual of [19704, 19546, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(3158, 9852, F3, 2, 26) (dual of [(9852, 2), 19546, 27]-NRT-code), using
(132, 158, 1783328)-Net in Base 3 — Upper bound on s
There is no (132, 158, 1783329)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2427 494959 006199 906474 169723 841899 968701 253136 116508 494565 272423 922652 883475 > 3158 [i]