Best Known (90, 90+14, s)-Nets in Base 3
(90, 90+14, 25310)-Net over F3 — Constructive and digital
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
(90, 90+14, 65183)-Net over F3 — Digital
Digital (90, 104, 65183)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3104, 65183, F3, 2, 14) (dual of [(65183, 2), 130262, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3104, 88586, F3, 2, 14) (dual of [(88586, 2), 177068, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3104, 177172, F3, 14) (dual of [177172, 177068, 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
- OOA 2-folding [i] based on linear OA(3104, 177172, F3, 14) (dual of [177172, 177068, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(3104, 88586, F3, 2, 14) (dual of [(88586, 2), 177068, 15]-NRT-code), using
(90, 90+14, large)-Net in Base 3 — Upper bound on s
There is no (90, 104, large)-net in base 3, because
- 12 times m-reduction [i] would yield (90, 92, large)-net in base 3, but