Best Known (110, 127, s)-Nets in Base 3
(110, 127, 22146)-Net over F3 — Constructive and digital
Digital (110, 127, 22146)-net over F3, using
- 31 times duplication [i] based on digital (109, 126, 22146)-net over F3, using
- net defined by OOA [i] based on linear OOA(3126, 22146, F3, 17, 17) (dual of [(22146, 17), 376356, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3126, 177169, F3, 17) (dual of [177169, 177043, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3126, 177173, F3, 17) (dual of [177173, 177047, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3126, 177173, F3, 17) (dual of [177173, 177047, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3126, 177169, F3, 17) (dual of [177169, 177043, 18]-code), using
- net defined by OOA [i] based on linear OOA(3126, 22146, F3, 17, 17) (dual of [(22146, 17), 376356, 18]-NRT-code), using
(110, 127, 59058)-Net over F3 — Digital
Digital (110, 127, 59058)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3127, 59058, F3, 3, 17) (dual of [(59058, 3), 177047, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3127, 177174, F3, 17) (dual of [177174, 177047, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3126, 177173, F3, 17) (dual of [177173, 177047, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(16) ⊂ Ce(13) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3126, 177173, F3, 17) (dual of [177173, 177047, 18]-code), using
- OOA 3-folding [i] based on linear OA(3127, 177174, F3, 17) (dual of [177174, 177047, 18]-code), using
(110, 127, large)-Net in Base 3 — Upper bound on s
There is no (110, 127, large)-net in base 3, because
- 15 times m-reduction [i] would yield (110, 112, large)-net in base 3, but