Best Known (34, 85, s)-Nets in Base 64
(34, 85, 513)-Net over F64 — Constructive and digital
Digital (34, 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
(34, 85, 189243)-Net in Base 64 — Upper bound on s
There is no (34, 85, 189244)-net in base 64, because
- 1 times m-reduction [i] would yield (34, 84, 189244)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 52 375988 813532 825910 058506 814339 788196 866424 876331 314564 326173 985397 654207 534386 358789 926862 513027 375175 449579 351045 684747 440542 796361 516190 109531 388971 > 6484 [i]