Best Known (42, 42+48, s)-Nets in Base 64
(42, 42+48, 513)-Net over F64 — Constructive and digital
Digital (42, 90, 513)-net over F64, using
- t-expansion [i] based on digital (28, 90, 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
(42, 42+48, 862)-Net over F64 — Digital
Digital (42, 90, 862)-net over F64, using
(42, 42+48, 922978)-Net in Base 64 — Upper bound on s
There is no (42, 90, 922979)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 3 599194 883289 643189 126911 136870 057343 548277 374650 516200 981086 722707 521418 640182 576955 786099 117418 537114 527816 121005 496285 841745 908527 841693 810166 075243 533516 117044 > 6490 [i]