Best Known (32, 45, s)-Nets in Base 49
(32, 45, 19660)-Net over F49 — Constructive and digital
Digital (32, 45, 19660)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (24, 37, 19608)-net over F49, using
- net defined by OOA [i] based on linear OOA(4937, 19608, F49, 13, 13) (dual of [(19608, 13), 254867, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4937, 117649, F49, 13) (dual of [117649, 117612, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(4937, 117649, F49, 13) (dual of [117649, 117612, 14]-code), using
- net defined by OOA [i] based on linear OOA(4937, 19608, F49, 13, 13) (dual of [(19608, 13), 254867, 14]-NRT-code), using
- digital (2, 8, 52)-net over F49, using
(32, 45, 240086)-Net over F49 — Digital
Digital (32, 45, 240086)-net over F49, using
(32, 45, large)-Net in Base 49 — Upper bound on s
There is no (32, 45, large)-net in base 49, because
- 11 times m-reduction [i] would yield (32, 34, large)-net in base 49, but