Best Known (168, 168+18, s)-Nets in Base 3
(168, 168+18, 932067)-Net over F3 — Constructive and digital
Digital (168, 186, 932067)-net over F3, using
- 32 times duplication [i] based on digital (166, 184, 932067)-net over F3, using
- t-expansion [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
- t-expansion [i] based on digital (165, 184, 932067)-net over F3, using
(168, 168+18, 2796203)-Net over F3 — Digital
Digital (168, 186, 2796203)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3186, 2796203, F3, 3, 18) (dual of [(2796203, 3), 8388423, 19]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3180, 2796201, F3, 3, 18) (dual of [(2796201, 3), 8388423, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 3-folding [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3180, 2796201, F3, 3, 18) (dual of [(2796201, 3), 8388423, 19]-NRT-code), using
(168, 168+18, large)-Net in Base 3 — Upper bound on s
There is no (168, 186, large)-net in base 3, because
- 16 times m-reduction [i] would yield (168, 170, large)-net in base 3, but