Best Known (49−7, 49, s)-Nets in Base 9
(49−7, 49, 2796200)-Net over F9 — Constructive and digital
Digital (42, 49, 2796200)-net over F9, using
- net defined by OOA [i] based on linear OOA(949, 2796200, F9, 7, 7) (dual of [(2796200, 7), 19573351, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(949, 8388601, F9, 7) (dual of [8388601, 8388552, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(949, large, F9, 7) (dual of [large, large−49, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 916−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(949, large, F9, 7) (dual of [large, large−49, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(949, 8388601, F9, 7) (dual of [8388601, 8388552, 8]-code), using
(49−7, 49, large)-Net over F9 — Digital
Digital (42, 49, large)-net over F9, using
- 92 times duplication [i] based on digital (40, 47, large)-net over F9, using
(49−7, 49, large)-Net in Base 9 — Upper bound on s
There is no (42, 49, large)-net in base 9, because
- 5 times m-reduction [i] would yield (42, 44, large)-net in base 9, but