Best Known (73−45, 73, s)-Nets in Base 64
(73−45, 73, 513)-Net over F64 — Constructive and digital
Digital (28, 73, 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
(73−45, 73, 117113)-Net in Base 64 — Upper bound on s
There is no (28, 73, 117114)-net in base 64, because
- 1 times m-reduction [i] would yield (28, 72, 117114)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 11091 862153 052662 385280 718474 747620 750912 283749 517659 142464 333693 171907 612840 641405 263402 628601 189836 285693 959678 506629 018924 470980 > 6472 [i]