Best Known (31, 31+60, s)-Nets in Base 64
(31, 31+60, 513)-Net over F64 — Constructive and digital
Digital (31, 91, 513)-net over F64, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(31, 31+60, 57554)-Net in Base 64 — Upper bound on s
There is no (31, 91, 57555)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 230 376262 962015 689062 440395 563313 662237 816706 008926 108779 700500 194419 630995 273101 996198 171677 522570 997312 650930 630671 186103 248609 053709 795848 172947 844273 788607 635120 > 6491 [i]