Best Known (74−14, 74, s)-Nets in Base 3
(74−14, 74, 938)-Net over F3 — Constructive and digital
Digital (60, 74, 938)-net over F3, using
- 31 times duplication [i] based on digital (59, 73, 938)-net over F3, using
- net defined by OOA [i] based on linear OOA(373, 938, F3, 14, 14) (dual of [(938, 14), 13059, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(373, 6566, F3, 14) (dual of [6566, 6493, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(373, 6569, F3, 14) (dual of [6569, 6496, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [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(365, 6561, F3, 13) (dual of [6561, 6496, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(373, 6569, F3, 14) (dual of [6569, 6496, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(373, 6566, F3, 14) (dual of [6566, 6493, 15]-code), using
- net defined by OOA [i] based on linear OOA(373, 938, F3, 14, 14) (dual of [(938, 14), 13059, 15]-NRT-code), using
(74−14, 74, 3248)-Net over F3 — Digital
Digital (60, 74, 3248)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(374, 3248, F3, 2, 14) (dual of [(3248, 2), 6422, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(374, 3285, F3, 2, 14) (dual of [(3285, 2), 6496, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(374, 6570, F3, 14) (dual of [6570, 6496, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(373, 6569, F3, 14) (dual of [6569, 6496, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [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(365, 6561, F3, 13) (dual of [6561, 6496, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(373, 6569, F3, 14) (dual of [6569, 6496, 15]-code), using
- OOA 2-folding [i] based on linear OA(374, 6570, F3, 14) (dual of [6570, 6496, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(374, 3285, F3, 2, 14) (dual of [(3285, 2), 6496, 15]-NRT-code), using
(74−14, 74, 186950)-Net in Base 3 — Upper bound on s
There is no (60, 74, 186951)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 202758 783006 801118 946114 586482 453907 > 374 [i]