Best Known (67−40, 67, s)-Nets in Base 64
(67−40, 67, 242)-Net over F64 — Constructive and digital
Digital (27, 67, 242)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 20, 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 (7, 47, 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 (0, 20, 65)-net over F64, using
(67−40, 67, 288)-Net in Base 64 — Constructive
(27, 67, 288)-net in base 64, using
- t-expansion [i] based on (22, 67, 288)-net in base 64, using
- 24 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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, 78, 288)-net over F128, using
- 24 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(67−40, 67, 425)-Net over F64 — Digital
Digital (27, 67, 425)-net over F64, using
- t-expansion [i] based on digital (26, 67, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
(67−40, 67, 513)-Net in Base 64
(27, 67, 513)-net in base 64, using
- 9 times m-reduction [i] based on (27, 76, 513)-net in base 64, using
- base change [i] based on digital (8, 57, 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, 57, 513)-net over F256, using
(67−40, 67, 148128)-Net in Base 64 — Upper bound on s
There is no (27, 67, 148129)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 10 329132 169635 564965 249514 993925 341462 955234 234870 268967 891349 072971 034469 774011 893705 454386 170080 832231 373102 695662 025896 > 6467 [i]