Best Known (69−39, 69, s)-Nets in Base 64
(69−39, 69, 513)-Net over F64 — Constructive and digital
Digital (30, 69, 513)-net over F64, using
- t-expansion [i] based on digital (28, 69, 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
(69−39, 69, 366510)-Net in Base 64 — Upper bound on s
There is no (30, 69, 366511)-net in base 64, because
- 1 times m-reduction [i] would yield (30, 68, 366511)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 661 056358 632950 070859 254628 258976 936670 005441 735828 871052 456543 230096 802535 216954 571476 846061 975794 310982 031730 055238 008840 > 6468 [i]