Best Known (45−25, 45, s)-Nets in Base 64
(45−25, 45, 257)-Net over F64 — Constructive and digital
Digital (20, 45, 257)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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, 32, 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, 13, 80)-net over F64, using
(45−25, 45, 288)-Net in Base 64 — Constructive
(20, 45, 288)-net in base 64, using
- 32 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
(45−25, 45, 391)-Net over F64 — Digital
Digital (20, 45, 391)-net over F64, using
(45−25, 45, 513)-Net in Base 64
(20, 45, 513)-net in base 64, using
- 3 times m-reduction [i] based on (20, 48, 513)-net in base 64, using
- base change [i] based on digital (8, 36, 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, 36, 513)-net over F256, using
(45−25, 45, 352106)-Net in Base 64 — Upper bound on s
There is no (20, 45, 352107)-net in base 64, because
- 1 times m-reduction [i] would yield (20, 44, 352107)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 29 643519 286554 975533 006156 973134 837754 543077 988824 838026 072614 807712 910824 132680 > 6444 [i]