Best Known (42, 42+13, s)-Nets in Base 49
(42, 42+13, 960850)-Net over F49 — Constructive and digital
Digital (42, 55, 960850)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (36, 49, 960800)-net over F49, using
- net defined by OOA [i] based on linear OOA(4949, 960800, F49, 13, 13) (dual of [(960800, 13), 12490351, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4949, 5764801, F49, 13) (dual of [5764801, 5764752, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, 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(4949, 5764801, F49, 13) (dual of [5764801, 5764752, 14]-code), using
- net defined by OOA [i] based on linear OOA(4949, 960800, F49, 13, 13) (dual of [(960800, 13), 12490351, 14]-NRT-code), using
- digital (0, 6, 50)-net over F49, using
(42, 42+13, 6149682)-Net over F49 — Digital
Digital (42, 55, 6149682)-net over F49, using
(42, 42+13, large)-Net in Base 49 — Upper bound on s
There is no (42, 55, large)-net in base 49, because
- 11 times m-reduction [i] would yield (42, 44, large)-net in base 49, but