Best Known (130, 130+19, s)-Nets in Base 9
(130, 130+19, 1864134)-Net over F9 — Constructive and digital
Digital (130, 149, 1864134)-net over F9, using
- net defined by OOA [i] based on linear OOA(9149, 1864134, F9, 21, 19) (dual of [(1864134, 21), 39146665, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(9149, 5592403, F9, 3, 19) (dual of [(5592403, 3), 16777060, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(9146, 5592402, F9, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- trace code [i] based on linear OOA(8173, 2796201, F81, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8173, large, F81, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, 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(8173, large, F81, 19) (dual of [large, large−73, 20]-code), using
- trace code [i] based on linear OOA(8173, 2796201, F81, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(9146, 5592402, F9, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(9149, 5592403, F9, 3, 19) (dual of [(5592403, 3), 16777060, 20]-NRT-code), using
(130, 130+19, large)-Net over F9 — Digital
Digital (130, 149, large)-net over F9, using
- 94 times duplication [i] based on digital (126, 145, large)-net over F9, using
- t-expansion [i] based on digital (124, 145, large)-net over F9, using
(130, 130+19, large)-Net in Base 9 — Upper bound on s
There is no (130, 149, large)-net in base 9, because
- 17 times m-reduction [i] would yield (130, 132, large)-net in base 9, but