Best Known (57−8, 57, s)-Nets in Base 9
(57−8, 57, 2097150)-Net over F9 — Constructive and digital
Digital (49, 57, 2097150)-net over F9, using
- net defined by OOA [i] based on linear OOA(957, 2097150, F9, 8, 8) (dual of [(2097150, 8), 16777143, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(957, 8388600, F9, 8) (dual of [8388600, 8388543, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(957, large, F9, 8) (dual of [large, large−57, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(957, large, F9, 8) (dual of [large, large−57, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(957, 8388600, F9, 8) (dual of [8388600, 8388543, 9]-code), using
(57−8, 57, large)-Net over F9 — Digital
Digital (49, 57, large)-net over F9, using
- 93 times duplication [i] based on digital (46, 54, large)-net over F9, using
(57−8, 57, large)-Net in Base 9 — Upper bound on s
There is no (49, 57, large)-net in base 9, because
- 6 times m-reduction [i] would yield (49, 51, large)-net in base 9, but