Best Known (47−26, 47, s)-Nets in Base 64
(47−26, 47, 257)-Net over F64 — Constructive and digital
Digital (21, 47, 257)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (7, 33, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (1, 14, 80)-net over F64, using
(47−26, 47, 288)-Net in Base 64 — Constructive
(21, 47, 288)-net in base 64, using
- 37 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
(47−26, 47, 414)-Net over F64 — Digital
Digital (21, 47, 414)-net over F64, using
(47−26, 47, 513)-Net in Base 64
(21, 47, 513)-net in base 64, using
- 5 times m-reduction [i] based on (21, 52, 513)-net in base 64, using
- base change [i] based on digital (8, 39, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 39, 513)-net over F256, using
(47−26, 47, 304854)-Net in Base 64 — Upper bound on s
There is no (21, 47, 304855)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 7 770965 048949 775660 636365 704825 456697 423269 387830 167340 058832 905391 124888 319998 480996 > 6447 [i]