Best Known (77−42, 77, s)-Nets in Base 64
(77−42, 77, 513)-Net over F64 — Constructive and digital
Digital (35, 77, 513)-net over F64, using
- t-expansion [i] based on digital (28, 77, 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
(77−42, 77, 653)-Net over F64 — Digital
Digital (35, 77, 653)-net over F64, using
(77−42, 77, 577835)-Net in Base 64 — Upper bound on s
There is no (35, 77, 577836)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 11 908778 707749 741203 761431 051456 271313 668856 933578 684528 516869 273846 433237 070392 126812 908169 911569 917843 640580 832206 010826 852575 214070 780764 > 6477 [i]