Best Known (169, 169+19, s)-Nets in Base 3
(169, 169+19, 932067)-Net over F3 — Constructive and digital
Digital (169, 188, 932067)-net over F3, using
- 34 times duplication [i] based on digital (165, 184, 932067)-net over F3, using
- net defined by OOA [i] based on linear OOA(3184, 932067, F3, 21, 19) (dual of [(932067, 21), 19573223, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3184, 2796202, F3, 3, 19) (dual of [(2796202, 3), 8388422, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 2796201, F3, 3, 19) (dual of [(2796201, 3), 8388422, 20]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 2796201, F3, 3, 19) (dual of [(2796201, 3), 8388422, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3184, 2796202, F3, 3, 19) (dual of [(2796202, 3), 8388422, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3184, 932067, F3, 21, 19) (dual of [(932067, 21), 19573223, 20]-NRT-code), using
(169, 169+19, 2461669)-Net over F3 — Digital
Digital (169, 188, 2461669)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3188, 2461669, F3, 3, 19) (dual of [(2461669, 3), 7384819, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3188, 2796203, F3, 3, 19) (dual of [(2796203, 3), 8388421, 20]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3187, 2796203, F3, 3, 19) (dual of [(2796203, 3), 8388422, 20]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3181, 2796201, F3, 3, 19) (dual of [(2796201, 3), 8388422, 20]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3181, 2796201, F3, 3, 19) (dual of [(2796201, 3), 8388422, 20]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3187, 2796203, F3, 3, 19) (dual of [(2796203, 3), 8388422, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3188, 2796203, F3, 3, 19) (dual of [(2796203, 3), 8388421, 20]-NRT-code), using
(169, 169+19, large)-Net in Base 3 — Upper bound on s
There is no (169, 188, large)-net in base 3, because
- 17 times m-reduction [i] would yield (169, 171, large)-net in base 3, but