Best Known (62, 62+14, s)-Nets in Base 3
(62, 62+14, 939)-Net over F3 — Constructive and digital
Digital (62, 76, 939)-net over F3, using
- net defined by OOA [i] based on linear OOA(376, 939, F3, 14, 14) (dual of [(939, 14), 13070, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(376, 6573, F3, 14) (dual of [6573, 6497, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(376, 6574, F3, 14) (dual of [6574, 6498, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(357, 6561, F3, 11) (dual of [6561, 6504, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(376, 6574, F3, 14) (dual of [6574, 6498, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(376, 6573, F3, 14) (dual of [6573, 6497, 15]-code), using
(62, 62+14, 3287)-Net over F3 — Digital
Digital (62, 76, 3287)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(376, 3287, F3, 2, 14) (dual of [(3287, 2), 6498, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(376, 6574, F3, 14) (dual of [6574, 6498, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(357, 6561, F3, 11) (dual of [6561, 6504, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(376, 6574, F3, 14) (dual of [6574, 6498, 15]-code), using
(62, 62+14, 255888)-Net in Base 3 — Upper bound on s
There is no (62, 76, 255889)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 824811 350614 206619 413858 133137 056459 > 376 [i]