Best Known (141, 141+20, s)-Nets in Base 3
(141, 141+20, 53146)-Net over F3 — Constructive and digital
Digital (141, 161, 53146)-net over F3, using
- net defined by OOA [i] based on linear OOA(3161, 53146, F3, 20, 20) (dual of [(53146, 20), 1062759, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3161, 531460, F3, 20) (dual of [531460, 531299, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3161, 531469, F3, 20) (dual of [531469, 531308, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(34, 28, F3, 2) (dual of [28, 24, 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(3161, 531469, F3, 20) (dual of [531469, 531308, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3161, 531460, F3, 20) (dual of [531460, 531299, 21]-code), using
(141, 141+20, 175002)-Net over F3 — Digital
Digital (141, 161, 175002)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3161, 175002, F3, 3, 20) (dual of [(175002, 3), 524845, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3161, 177156, F3, 3, 20) (dual of [(177156, 3), 531307, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3161, 531468, F3, 20) (dual of [531468, 531307, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3161, 531469, F3, 20) (dual of [531469, 531308, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(34, 28, F3, 2) (dual of [28, 24, 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(3161, 531469, F3, 20) (dual of [531469, 531308, 21]-code), using
- OOA 3-folding [i] based on linear OA(3161, 531468, F3, 20) (dual of [531468, 531307, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(3161, 177156, F3, 3, 20) (dual of [(177156, 3), 531307, 21]-NRT-code), using
(141, 141+20, large)-Net in Base 3 — Upper bound on s
There is no (141, 161, large)-net in base 3, because
- 18 times m-reduction [i] would yield (141, 143, large)-net in base 3, but