Best Known (47−10, 47, s)-Nets in Base 49
(47−10, 47, 1677720)-Net over F49 — Constructive and digital
Digital (37, 47, 1677720)-net over F49, using
- 491 times duplication [i] based on digital (36, 46, 1677720)-net over F49, using
- net defined by OOA [i] based on linear OOA(4946, 1677720, F49, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4946, 8388600, F49, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4946, large, F49, 10) (dual of [large, large−46, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 25679568 | 495−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(4946, large, F49, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(4946, 8388600, F49, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(4946, 1677720, F49, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
(47−10, 47, large)-Net over F49 — Digital
Digital (37, 47, large)-net over F49, using
- 1 times m-reduction [i] based on digital (37, 48, large)-net over F49, using
(47−10, 47, large)-Net in Base 49 — Upper bound on s
There is no (37, 47, large)-net in base 49, because
- 8 times m-reduction [i] would yield (37, 39, large)-net in base 49, but