Best Known (47−28, 47, s)-Nets in Base 64
(47−28, 47, 193)-Net over F64 — Constructive and digital
Digital (19, 47, 193)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 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 (5, 33, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- digital (0, 14, 65)-net over F64, using
(47−28, 47, 288)-Net in Base 64 — Constructive
(19, 47, 288)-net in base 64, using
- 23 times m-reduction [i] based on (19, 70, 288)-net in base 64, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
(47−28, 47, 315)-Net over F64 — Digital
Digital (19, 47, 315)-net over F64, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 19 and N(F) ≥ 315, using
(47−28, 47, 321)-Net in Base 64
(19, 47, 321)-net in base 64, using
- 2 times m-reduction [i] based on (19, 49, 321)-net in base 64, using
- base change [i] based on digital (12, 42, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- base change [i] based on digital (12, 42, 321)-net over F128, using
(47−28, 47, 111095)-Net in Base 64 — Upper bound on s
There is no (19, 47, 111096)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 7 771505 108300 330421 132923 173190 066902 062186 620661 265211 886726 818233 912758 372466 765786 > 6447 [i]