Best Known (129, 142, s)-Nets in Base 9
(129, 142, 5592402)-Net over F9 — Constructive and digital
Digital (129, 142, 5592402)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (35, 41, 2796201)-net over F9, using
- net defined by OOA [i] based on linear OOA(941, 2796201, F9, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(941, large, F9, 6) (dual of [large, large−41, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(941, large, F9, 6) (dual of [large, large−41, 7]-code), using
- net defined by OOA [i] based on linear OOA(941, 2796201, F9, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
- digital (88, 101, 2796201)-net over F9, using
- net defined by OOA [i] based on linear OOA(9101, 2796201, F9, 15, 13) (dual of [(2796201, 15), 41942914, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9101, 5592403, F9, 3, 13) (dual of [(5592403, 3), 16777108, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(998, 5592402, F9, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(998, 5592402, F9, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9101, 5592403, F9, 3, 13) (dual of [(5592403, 3), 16777108, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(9101, 2796201, F9, 15, 13) (dual of [(2796201, 15), 41942914, 14]-NRT-code), using
- digital (35, 41, 2796201)-net over F9, using
(129, 142, large)-Net over F9 — Digital
Digital (129, 142, large)-net over F9, using
- t-expansion [i] based on digital (124, 142, large)-net over F9, using
- 3 times m-reduction [i] based on digital (124, 145, large)-net over F9, using
(129, 142, large)-Net in Base 9 — Upper bound on s
There is no (129, 142, large)-net in base 9, because
- 11 times m-reduction [i] would yield (129, 131, large)-net in base 9, but