Best Known (16, 16+5, s)-Nets in Base 49
(16, 16+5, 4194301)-Net over F49 — Constructive and digital
Digital (16, 21, 4194301)-net over F49, using
- net defined by OOA [i] based on linear OOA(4921, 4194301, F49, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(4921, large, F49, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 28247525 | 4910−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(4921, large, F49, 5) (dual of [large, large−21, 6]-code), using
(16, 16+5, large)-Net over F49 — Digital
Digital (16, 21, large)-net over F49, using
- 491 times duplication [i] based on digital (15, 20, large)-net over F49, using
(16, 16+5, large)-Net in Base 49 — Upper bound on s
There is no (16, 21, large)-net in base 49, because
- 3 times m-reduction [i] would yield (16, 18, large)-net in base 49, but