Best Known (155, 155+24, s)-Nets in Base 3
(155, 155+24, 14764)-Net over F3 — Constructive and digital
Digital (155, 179, 14764)-net over F3, using
- 31 times duplication [i] based on digital (154, 178, 14764)-net over F3, using
- net defined by OOA [i] based on linear OOA(3178, 14764, F3, 24, 24) (dual of [(14764, 24), 354158, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3178, 177168, F3, 24) (dual of [177168, 176990, 25]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(3178, 177170, F3, 24) (dual of [177170, 176992, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3178, 177168, F3, 24) (dual of [177168, 176990, 25]-code), using
- net defined by OOA [i] based on linear OOA(3178, 14764, F3, 24, 24) (dual of [(14764, 24), 354158, 25]-NRT-code), using
(155, 155+24, 59057)-Net over F3 — Digital
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
(155, 155+24, large)-Net in Base 3 — Upper bound on s
There is no (155, 179, large)-net in base 3, because
- 22 times m-reduction [i] would yield (155, 157, large)-net in base 3, but