MinT - Best Known (68−61, 68, s)-Nets in Base 64

Best Known (68−61, 68, s)-Nets in Base 64

(68−61, 68, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 68, 177)-net over F₆₄, using

net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]

(68−61, 68, 2051)-Net in Base 64 — Upper bound on s

There is no (7, 68, 2052)-net in base 64, because

1 times m-reduction [i] would yield (7, 67, 2052)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 10 386879 765423 738991 154286 812342 537564 870121 736907 292012 450574 104693 795851 306824 907125 093077 697805 200673 753920 336935 815680 > 64⁶⁷ [i]