Best Known (131−19, 131, s)-Nets in Base 9
(131−19, 131, 932066)-Net over F9 — Constructive and digital
Digital (112, 131, 932066)-net over F9, using
- 92 times duplication [i] based on digital (110, 129, 932066)-net over F9, using
- net defined by OOA [i] based on linear OOA(9129, 932066, F9, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9129, 8388595, F9, 19) (dual of [8388595, 8388466, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 916−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9129, 8388595, F9, 19) (dual of [8388595, 8388466, 20]-code), using
- net defined by OOA [i] based on linear OOA(9129, 932066, F9, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
(131−19, 131, large)-Net over F9 — Digital
Digital (112, 131, large)-net over F9, using
- 92 times duplication [i] based on digital (110, 129, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 916−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
(131−19, 131, large)-Net in Base 9 — Upper bound on s
There is no (112, 131, large)-net in base 9, because
- 17 times m-reduction [i] would yield (112, 114, large)-net in base 9, but