Best Known (84−44, 84, s)-Nets in Base 64
(84−44, 84, 513)-Net over F64 — Constructive and digital
Digital (40, 84, 513)-net over F64, using
- t-expansion [i] based on digital (28, 84, 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
(84−44, 84, 926)-Net over F64 — Digital
Digital (40, 84, 926)-net over F64, using
(84−44, 84, 1131962)-Net in Base 64 — Upper bound on s
There is no (40, 84, 1131963)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 52 375256 353896 990968 507294 164969 887947 081161 112015 436177 060417 674220 112488 614209 118704 685954 441843 915094 663162 815769 946787 873804 316051 810746 776045 151938 > 6484 [i]