Best Known (156, 156+24, s)-Nets in Base 3
(156, 156+24, 14764)-Net over F3 — Constructive and digital
Digital (156, 180, 14764)-net over F3, using
- 1 times m-reduction [i] based on digital (156, 181, 14764)-net over F3, using
- net defined by OOA [i] based on linear OOA(3181, 14764, F3, 25, 25) (dual of [(14764, 25), 368919, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3181, 177169, F3, 25) (dual of [177169, 176988, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, 177173, F3, 25) (dual of [177173, 176992, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(34, 26, F3, 2) (dual of [26, 22, 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(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3181, 177173, F3, 25) (dual of [177173, 176992, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3181, 177169, F3, 25) (dual of [177169, 176988, 26]-code), using
- net defined by OOA [i] based on linear OOA(3181, 14764, F3, 25, 25) (dual of [(14764, 25), 368919, 26]-NRT-code), using
(156, 156+24, 59057)-Net over F3 — Digital
Digital (156, 180, 59057)-net over F3, using
- 31 times duplication [i] based on digital (155, 179, 59057)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3179, 59057, F3, 3, 24) (dual of [(59057, 3), 176992, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3179, 177171, F3, 24) (dual of [177171, 176992, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3178, 177170, F3, 24) (dual of [177170, 176992, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(31, 23, F3, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3178, 177170, F3, 24) (dual of [177170, 176992, 25]-code), using
- OOA 3-folding [i] based on linear OA(3179, 177171, F3, 24) (dual of [177171, 176992, 25]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3179, 59057, F3, 3, 24) (dual of [(59057, 3), 176992, 25]-NRT-code), using
(156, 156+24, large)-Net in Base 3 — Upper bound on s
There is no (156, 180, large)-net in base 3, because
- 22 times m-reduction [i] would yield (156, 158, large)-net in base 3, but