Best Known (30, 75, s)-Nets in Base 64
(30, 75, 513)-Net over F64 — Constructive and digital
Digital (30, 75, 513)-net over F64, using
- t-expansion [i] based on digital (28, 75, 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
(30, 75, 170929)-Net in Base 64 — Upper bound on s
There is no (30, 75, 170930)-net in base 64, because
- 1 times m-reduction [i] would yield (30, 74, 170930)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 45 429122 136067 207544 856701 442854 151812 827918 829648 623479 342851 765873 529075 363905 736388 736473 633039 738207 360011 334563 178155 013050 226576 > 6474 [i]