MinT - Best Known (51−43, 51, s)-Nets in Base 64

Best Known (51−43, 51, s)-Nets in Base 64

(51−43, 51, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 51, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 51, 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]

(51−43, 51, 2741)-Net in Base 64 — Upper bound on s

There is no (8, 51, 2742)-net in base 64, because

1 times m-reduction [i] would yield (8, 50, 2742)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 048816 745011 385614 370567 955716 521089 060881 809716 102435 643347 326648 792217 845179 578852 422673 > 64⁵⁰ [i]