Best Known (234, 247, s)-Nets in Base 3
(234, 247, 6990511)-Net over F3 — Constructive and digital
Digital (234, 247, 6990511)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (58, 64, 2796211)-net over F3, using
- net defined by OOA [i] based on linear OOA(364, 2796211, F3, 6, 6) (dual of [(2796211, 6), 16777202, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(364, 2796211, F3, 5, 6) (dual of [(2796211, 5), 13980991, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(34, 10, F3, 5, 3) (dual of [(10, 5), 46, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(34, 10, F3, 3, 3) (dual of [(10, 3), 26, 4]-NRT-code), using
- linear OOA(360, 2796201, F3, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- linear OOA(34, 10, F3, 5, 3) (dual of [(10, 5), 46, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(364, 2796211, F3, 5, 6) (dual of [(2796211, 5), 13980991, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(364, 2796211, F3, 6, 6) (dual of [(2796211, 6), 16777202, 7]-NRT-code), using
- digital (170, 183, 4194300)-net over F3, using
- trace code for nets [i] based on digital (48, 61, 1398100)-net over F27, using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- trace code for nets [i] based on digital (48, 61, 1398100)-net over F27, using
- digital (58, 64, 2796211)-net over F3, using
(234, 247, large)-Net over F3 — Digital
Digital (234, 247, large)-net over F3, using
- 36 times duplication [i] based on digital (228, 241, large)-net over F3, using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
(234, 247, large)-Net in Base 3 — Upper bound on s
There is no (234, 247, large)-net in base 3, because
- 11 times m-reduction [i] would yield (234, 236, large)-net in base 3, but