Best Known (164, 183, s)-Nets in Base 3
(164, 183, 932066)-Net over F3 — Constructive and digital
Digital (164, 183, 932066)-net over F3, using
- 32 times duplication [i] based on digital (162, 181, 932066)-net over F3, using
- net defined by OOA [i] based on linear OOA(3181, 932066, F3, 19, 19) (dual of [(932066, 19), 17709073, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3181, 8388595, F3, 19) (dual of [8388595, 8388414, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3181, 8388595, F3, 19) (dual of [8388595, 8388414, 20]-code), using
- net defined by OOA [i] based on linear OOA(3181, 932066, F3, 19, 19) (dual of [(932066, 19), 17709073, 20]-NRT-code), using
(164, 183, 2097151)-Net over F3 — Digital
Digital (164, 183, 2097151)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3183, 2097151, F3, 4, 19) (dual of [(2097151, 4), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3183, 4194302, F3, 2, 19) (dual of [(4194302, 2), 8388421, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3183, 4194302, F3, 2, 19) (dual of [(4194302, 2), 8388421, 20]-NRT-code), using
(164, 183, large)-Net in Base 3 — Upper bound on s
There is no (164, 183, large)-net in base 3, because
- 17 times m-reduction [i] would yield (164, 166, large)-net in base 3, but