Best Known (23, 59, s)-Nets in Base 64
(23, 59, 193)-Net over F64 — Constructive and digital
Digital (23, 59, 193)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 18, 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, 41, 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, 18, 65)-net over F64, using
(23, 59, 288)-Net in Base 64 — Constructive
(23, 59, 288)-net in base 64, using
- t-expansion [i] based on (22, 59, 288)-net in base 64, using
- 32 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
- 32 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(23, 59, 342)-Net over F64 — Digital
Digital (23, 59, 342)-net over F64, using
- t-expansion [i] based on digital (20, 59, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
(23, 59, 513)-Net in Base 64
(23, 59, 513)-net in base 64, using
- 1 times m-reduction [i] based on (23, 60, 513)-net in base 64, using
- base change [i] based on digital (8, 45, 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, 45, 513)-net over F256, using
(23, 59, 99771)-Net in Base 64 — Upper bound on s
There is no (23, 59, 99772)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 36697 240414 237334 081765 733912 904453 675955 129635 129490 192598 702068 968616 279944 092443 230678 678789 220651 324503 > 6459 [i]