Best Known (86−52, 86, s)-Nets in Base 64
(86−52, 86, 513)-Net over F64 — Constructive and digital
Digital (34, 86, 513)-net over F64, using
- t-expansion [i] based on digital (28, 86, 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
(86−52, 86, 157835)-Net in Base 64 — Upper bound on s
There is no (34, 86, 157836)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 214544 164488 095997 218374 411187 573050 532236 377194 656363 586632 140103 546399 053764 840598 889227 607384 648580 550629 919520 389511 165104 688572 229307 937447 915702 913432 > 6486 [i]