Best Known (48, 56, s)-Nets in Base 7
(48, 56, 2097150)-Net over F7 — Constructive and digital
Digital (48, 56, 2097150)-net over F7, using
- 71 times duplication [i] based on digital (47, 55, 2097150)-net over F7, using
- net defined by OOA [i] based on linear OOA(755, 2097150, F7, 8, 8) (dual of [(2097150, 8), 16777145, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(755, 8388600, F7, 8) (dual of [8388600, 8388545, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 20176803 | 79−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(755, 8388600, F7, 8) (dual of [8388600, 8388545, 9]-code), using
- net defined by OOA [i] based on linear OOA(755, 2097150, F7, 8, 8) (dual of [(2097150, 8), 16777145, 9]-NRT-code), using
(48, 56, large)-Net over F7 — Digital
Digital (48, 56, large)-net over F7, using
- 71 times duplication [i] based on digital (47, 55, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 20176803 | 79−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-code), using
(48, 56, large)-Net in Base 7 — Upper bound on s
There is no (48, 56, large)-net in base 7, because
- 6 times m-reduction [i] would yield (48, 50, large)-net in base 7, but