Best Known (74−45, 74, s)-Nets in Base 64
(74−45, 74, 513)-Net over F64 — Constructive and digital
Digital (29, 74, 513)-net over F64, using
- t-expansion [i] based on digital (28, 74, 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
(74−45, 74, 141485)-Net in Base 64 — Upper bound on s
There is no (29, 74, 141486)-net in base 64, because
- 1 times m-reduction [i] would yield (29, 73, 141486)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 709830 094786 782930 286137 536114 326463 087709 516599 857692 000106 102803 472072 188028 654904 170454 449213 800087 827213 652631 441892 986534 841656 > 6473 [i]