Best Known (121, 133, s)-Nets in Base 3
(121, 133, 1398142)-Net over F3 — Constructive and digital
Digital (121, 133, 1398142)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 13, 42)-net over F3, using
- digital (108, 120, 1398100)-net over F3, using
- net defined by OOA [i] based on linear OOA(3120, 1398100, F3, 12, 12) (dual of [(1398100, 12), 16777080, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3120, 8388600, F3, 12) (dual of [8388600, 8388480, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3120, 8388600, F3, 12) (dual of [8388600, 8388480, 13]-code), using
- net defined by OOA [i] based on linear OOA(3120, 1398100, F3, 12, 12) (dual of [(1398100, 12), 16777080, 13]-NRT-code), using
(121, 133, 4497239)-Net over F3 — Digital
Digital (121, 133, 4497239)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3133, 4497239, F3, 12) (dual of [4497239, 4497106, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3133, large, F3, 12) (dual of [large, large−133, 13]-code), using
- 13 times code embedding in larger space [i] based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 13 times code embedding in larger space [i] based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3133, large, F3, 12) (dual of [large, large−133, 13]-code), using
(121, 133, large)-Net in Base 3 — Upper bound on s
There is no (121, 133, large)-net in base 3, because
- 10 times m-reduction [i] would yield (121, 123, large)-net in base 3, but