Best Known (85−52, 85, s)-Nets in Base 64
(85−52, 85, 513)-Net over F64 — Constructive and digital
Digital (33, 85, 513)-net over F64, using
- t-expansion [i] based on digital (28, 85, 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
(85−52, 85, 134502)-Net in Base 64 — Upper bound on s
There is no (33, 85, 134503)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 3352 358595 561700 356849 973146 388918 917941 970178 414442 249164 875629 902276 642727 492272 870139 185886 395062 172143 742411 277316 365962 557135 822182 768012 577249 499060 > 6485 [i]