Best Known (163, 163+18, s)-Nets in Base 3
(163, 163+18, 932067)-Net over F3 — Constructive and digital
Digital (163, 181, 932067)-net over F3, using
- 31 times duplication [i] based on digital (162, 180, 932067)-net over F3, using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- OA 9-folding and stacking [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]
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
(163, 163+18, 2796201)-Net over F3 — Digital
Digital (163, 181, 2796201)-net over F3, using
- 31 times duplication [i] based on digital (162, 180, 2796201)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [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
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3180, 2796201, F3, 3, 18) (dual of [(2796201, 3), 8388423, 19]-NRT-code), using
(163, 163+18, large)-Net in Base 3 — Upper bound on s
There is no (163, 181, large)-net in base 3, because
- 16 times m-reduction [i] would yield (163, 165, large)-net in base 3, but