Best Known (50−15, 50, s)-Nets in Base 64
(50−15, 50, 37514)-Net over F64 — Constructive and digital
Digital (35, 50, 37514)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (28, 43, 37449)-net over F64, using
- net defined by OOA [i] based on linear OOA(6443, 37449, F64, 15, 15) (dual of [(37449, 15), 561692, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using
- net defined by OOA [i] based on linear OOA(6443, 37449, F64, 15, 15) (dual of [(37449, 15), 561692, 16]-NRT-code), using
- digital (0, 7, 65)-net over F64, using
(50−15, 50, 270876)-Net over F64 — Digital
Digital (35, 50, 270876)-net over F64, using
(50−15, 50, large)-Net in Base 64 — Upper bound on s
There is no (35, 50, large)-net in base 64, because
- 13 times m-reduction [i] would yield (35, 37, large)-net in base 64, but