Best Known (82−12, 82, s)-Nets in Base 9
(82−12, 82, 1398100)-Net over F9 — Constructive and digital
Digital (70, 82, 1398100)-net over F9, using
- 91 times duplication [i] based on digital (69, 81, 1398100)-net over F9, using
- net defined by OOA [i] based on linear OOA(981, 1398100, F9, 12, 12) (dual of [(1398100, 12), 16777119, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(981, 8388600, F9, 12) (dual of [8388600, 8388519, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(981, large, F9, 12) (dual of [large, large−81, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(981, large, F9, 12) (dual of [large, large−81, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(981, 8388600, F9, 12) (dual of [8388600, 8388519, 13]-code), using
- net defined by OOA [i] based on linear OOA(981, 1398100, F9, 12, 12) (dual of [(1398100, 12), 16777119, 13]-NRT-code), using
(82−12, 82, large)-Net over F9 — Digital
Digital (70, 82, large)-net over F9, using
- 91 times duplication [i] based on digital (69, 81, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(981, large, F9, 12) (dual of [large, large−81, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(981, large, F9, 12) (dual of [large, large−81, 13]-code), using
(82−12, 82, large)-Net in Base 9 — Upper bound on s
There is no (70, 82, large)-net in base 9, because
- 10 times m-reduction [i] would yield (70, 72, large)-net in base 9, but