Best Known (51−15, 51, s)-Nets in Base 49
(51−15, 51, 16858)-Net over F49 — Constructive and digital
Digital (36, 51, 16858)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (28, 43, 16807)-net over F49, using
- net defined by OOA [i] based on linear OOA(4943, 16807, F49, 15, 15) (dual of [(16807, 15), 252062, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using
- net defined by OOA [i] based on linear OOA(4943, 16807, F49, 15, 15) (dual of [(16807, 15), 252062, 16]-NRT-code), using
- digital (1, 8, 51)-net over F49, using
(51−15, 51, 180874)-Net over F49 — Digital
Digital (36, 51, 180874)-net over F49, using
(51−15, 51, large)-Net in Base 49 — Upper bound on s
There is no (36, 51, large)-net in base 49, because
- 13 times m-reduction [i] would yield (36, 38, large)-net in base 49, but