Best Known (81, 94, s)-Nets in Base 3
(81, 94, 29528)-Net over F3 — Constructive and digital
Digital (81, 94, 29528)-net over F3, using
- 31 times duplication [i] based on digital (80, 93, 29528)-net over F3, using
- net defined by OOA [i] based on linear OOA(393, 29528, F3, 13, 13) (dual of [(29528, 13), 383771, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(393, 177169, F3, 13) (dual of [177169, 177076, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(393, 177173, F3, 13) (dual of [177173, 177080, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(367, 177147, F3, 10) (dual of [177147, 177080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(393, 177173, F3, 13) (dual of [177173, 177080, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(393, 177169, F3, 13) (dual of [177169, 177076, 14]-code), using
- net defined by OOA [i] based on linear OOA(393, 29528, F3, 13, 13) (dual of [(29528, 13), 383771, 14]-NRT-code), using
(81, 94, 59058)-Net over F3 — Digital
Digital (81, 94, 59058)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(394, 59058, F3, 3, 13) (dual of [(59058, 3), 177080, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(394, 177174, F3, 13) (dual of [177174, 177080, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(393, 177173, F3, 13) (dual of [177173, 177080, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(367, 177147, F3, 10) (dual of [177147, 177080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(12) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(393, 177173, F3, 13) (dual of [177173, 177080, 14]-code), using
- OOA 3-folding [i] based on linear OA(394, 177174, F3, 13) (dual of [177174, 177080, 14]-code), using
(81, 94, large)-Net in Base 3 — Upper bound on s
There is no (81, 94, large)-net in base 3, because
- 11 times m-reduction [i] would yield (81, 83, large)-net in base 3, but