Best Known (45, 45+19, s)-Nets in Base 64
(45, 45+19, 29192)-Net over F64 — Constructive and digital
Digital (45, 64, 29192)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (36, 55, 29127)-net over F64, using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
- digital (0, 9, 65)-net over F64, using
(45, 45+19, 316793)-Net over F64 — Digital
Digital (45, 64, 316793)-net over F64, using
(45, 45+19, large)-Net in Base 64 — Upper bound on s
There is no (45, 64, large)-net in base 64, because
- 17 times m-reduction [i] would yield (45, 47, large)-net in base 64, but