MinT - Best Known (73−65, 73, s)-Nets in Base 64

Best Known (73−65, 73, s)-Nets in Base 64

(73−65, 73, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 73, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 73, 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]

(73−65, 73, 2336)-Net in Base 64 — Upper bound on s

There is no (8, 73, 2337)-net in base 64, because

1 times m-reduction [i] would yield (8, 72, 2337)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11234 335719 917246 946615 526008 191593 105571 438615 211813 967932 949514 326857 142724 769894 845805 358750 896567 478964 205712 243805 428293 140185 > 64⁷² [i]