Best Known (81−49, 81, s)-Nets in Base 64
(81−49, 81, 513)-Net over F64 — Constructive and digital
Digital (32, 81, 513)-net over F64, using
- t-expansion [i] based on digital (28, 81, 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
(81−49, 81, 163151)-Net in Base 64 — Upper bound on s
There is no (32, 81, 163152)-net in base 64, because
- 1 times m-reduction [i] would yield (32, 80, 163152)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 122080 861518 448831 733327 728099 046038 901124 228605 937675 823677 653932 364259 960386 985130 109837 378167 182475 455599 500677 139587 424965 375606 759784 219564 > 6480 [i]