Best Known (130−12, 130, s)-Nets in Base 3
(130−12, 130, 1398119)-Net over F3 — Constructive and digital
Digital (118, 130, 1398119)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 19)-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
(130−12, 130, 4194320)-Net over F3 — Digital
Digital (118, 130, 4194320)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3130, 4194320, F3, 2, 12) (dual of [(4194320, 2), 8388510, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(310, 19, F3, 2, 6) (dual of [(19, 2), 28, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 10, 19)-net over F3, using
- linear OOA(3120, 4194301, F3, 2, 12) (dual of [(4194301, 2), 8388482, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3120, 8388602, F3, 12) (dual of [8388602, 8388482, 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
- OOA 2-folding [i] based on linear OA(3120, 8388602, F3, 12) (dual of [8388602, 8388482, 13]-code), using
- linear OOA(310, 19, F3, 2, 6) (dual of [(19, 2), 28, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
(130−12, 130, large)-Net in Base 3 — Upper bound on s
There is no (118, 130, large)-net in base 3, because
- 10 times m-reduction [i] would yield (118, 120, large)-net in base 3, but