Best Known (51−11, 51, s)-Nets in Base 49
(51−11, 51, 1677720)-Net over F49 — Constructive and digital
Digital (40, 51, 1677720)-net over F49, using
- net defined by OOA [i] based on linear OOA(4951, 1677720, F49, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4951, 8388601, F49, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4951, large, F49, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 28247525 | 4910−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4951, large, F49, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4951, 8388601, F49, 11) (dual of [8388601, 8388550, 12]-code), using
(51−11, 51, large)-Net over F49 — Digital
Digital (40, 51, large)-net over F49, using
- 1 times m-reduction [i] based on digital (40, 52, large)-net over F49, using
(51−11, 51, large)-Net in Base 49 — Upper bound on s
There is no (40, 51, large)-net in base 49, because
- 9 times m-reduction [i] would yield (40, 42, large)-net in base 49, but