Best Known (41−9, 41, s)-Nets in Base 49
(41−9, 41, 2097150)-Net over F49 — Constructive and digital
Digital (32, 41, 2097150)-net over F49, using
- net defined by OOA [i] based on linear OOA(4941, 2097150, F49, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(4941, 8388601, F49, 9) (dual of [8388601, 8388560, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(4941, large, F49, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 28247525 | 4910−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4941, large, F49, 9) (dual of [large, large−41, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(4941, 8388601, F49, 9) (dual of [8388601, 8388560, 10]-code), using
(41−9, 41, large)-Net over F49 — Digital
Digital (32, 41, large)-net over F49, using
- 492 times duplication [i] based on digital (30, 39, large)-net over F49, using
(41−9, 41, large)-Net in Base 49 — Upper bound on s
There is no (32, 41, large)-net in base 49, because
- 7 times m-reduction [i] would yield (32, 34, large)-net in base 49, but