Best Known (16−4, 16, s)-Nets in Base 49
(16−4, 16, 4194301)-Net over F49 — Constructive and digital
Digital (12, 16, 4194301)-net over F49, using
- net defined by OOA [i] based on linear OOA(4916, 4194301, F49, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4916, 4194301, F49, 3, 4) (dual of [(4194301, 3), 12582887, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(4916, 8388602, F49, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4916, large, F49, 4) (dual of [large, large−16, 5]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 25679568 | 495−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(4916, large, F49, 4) (dual of [large, large−16, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(4916, 8388602, F49, 4) (dual of [8388602, 8388586, 5]-code), using
- appending kth column [i] based on linear OOA(4916, 4194301, F49, 3, 4) (dual of [(4194301, 3), 12582887, 5]-NRT-code), using
(16−4, 16, large)-Net over F49 — Digital
Digital (12, 16, large)-net over F49, using
- 491 times duplication [i] based on digital (11, 15, large)-net over F49, using
- net defined by OOA [i] based on linear OOA(4915, large, F49, 4, 4), using
- appending kth column [i] based on linear OOA(4915, large, F49, 3, 4), using
- net defined by OOA [i] based on linear OOA(4915, large, F49, 4, 4), using
(16−4, 16, large)-Net in Base 49 — Upper bound on s
There is no (12, 16, large)-net in base 49, because
- 2 times m-reduction [i] would yield (12, 14, large)-net in base 49, but