Best Known (91, 91+14, s)-Nets in Base 3
(91, 91+14, 25310)-Net over F3 — Constructive and digital
Digital (91, 105, 25310)-net over F3, using
- 31 times duplication [i] based on digital (90, 104, 25310)-net over F3, using
- net defined by OOA [i] based on linear OOA(3104, 25310, F3, 14, 14) (dual of [(25310, 14), 354236, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3104, 177170, F3, 14) (dual of [177170, 177066, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3104, 177173, F3, 14) (dual of [177173, 177069, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- 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(378, 177147, F3, 11) (dual of [177147, 177069, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3104, 177173, F3, 14) (dual of [177173, 177069, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3104, 177170, F3, 14) (dual of [177170, 177066, 15]-code), using
- net defined by OOA [i] based on linear OOA(3104, 25310, F3, 14, 14) (dual of [(25310, 14), 354236, 15]-NRT-code), using
(91, 91+14, 72030)-Net over F3 — Digital
Digital (91, 105, 72030)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3105, 72030, F3, 2, 14) (dual of [(72030, 2), 143955, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3105, 88587, F3, 2, 14) (dual of [(88587, 2), 177069, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3105, 177174, F3, 14) (dual of [177174, 177069, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3104, 177173, F3, 14) (dual of [177173, 177069, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- 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(378, 177147, F3, 11) (dual of [177147, 177069, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3104, 177173, F3, 14) (dual of [177173, 177069, 15]-code), using
- OOA 2-folding [i] based on linear OA(3105, 177174, F3, 14) (dual of [177174, 177069, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(3105, 88587, F3, 2, 14) (dual of [(88587, 2), 177069, 15]-NRT-code), using
(91, 91+14, large)-Net in Base 3 — Upper bound on s
There is no (91, 105, large)-net in base 3, because
- 12 times m-reduction [i] would yield (91, 93, large)-net in base 3, but