Best Known (39, 39+48, s)-Nets in Base 64
(39, 39+48, 513)-Net over F64 — Constructive and digital
Digital (39, 87, 513)-net over F64, using
- t-expansion [i] based on digital (28, 87, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(39, 39+48, 660)-Net over F64 — Digital
Digital (39, 87, 660)-net over F64, using
(39, 39+48, 548801)-Net in Base 64 — Upper bound on s
There is no (39, 87, 548802)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 13 729970 709523 997314 636809 102582 748229 404542 216255 657420 699460 961925 552605 627903 108081 739631 230682 651137 808937 534764 741756 063365 181854 294497 884066 645661 827384 > 6487 [i]