Best Known (28, 28+63, s)-Nets in Base 64
(28, 28+63, 513)-Net over F64 — Constructive and digital
Digital (28, 91, 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
(28, 28+63, 34533)-Net in Base 64 — Upper bound on s
There is no (28, 91, 34534)-net in base 64, because
- 1 times m-reduction [i] would yield (28, 90, 34534)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 599369 250091 760728 869570 285458 911890 253836 934766 560436 282983 065214 132951 605671 526942 999623 092675 885755 513851 454064 640107 878308 857810 215519 083767 601591 507698 343152 > 6490 [i]