Best Known (131, 148, s)-Nets in Base 3
(131, 148, 199294)-Net over F3 — Constructive and digital
Digital (131, 148, 199294)-net over F3, using
- net defined by OOA [i] based on linear OOA(3148, 199294, F3, 17, 17) (dual of [(199294, 17), 3387850, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3148, 1594353, F3, 17) (dual of [1594353, 1594205, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- 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(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(16) ⊂ Ce(13) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(3148, 1594353, F3, 17) (dual of [1594353, 1594205, 18]-code), using
(131, 148, 531451)-Net over F3 — Digital
Digital (131, 148, 531451)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3148, 531451, F3, 3, 17) (dual of [(531451, 3), 1594205, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3148, 1594353, F3, 17) (dual of [1594353, 1594205, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- 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(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(16) ⊂ Ce(13) [i] based on
- OOA 3-folding [i] based on linear OA(3148, 1594353, F3, 17) (dual of [1594353, 1594205, 18]-code), using
(131, 148, large)-Net in Base 3 — Upper bound on s
There is no (131, 148, large)-net in base 3, because
- 15 times m-reduction [i] would yield (131, 133, large)-net in base 3, but