MinT - Best Known (37−29, 37, s)-Nets in Base 64

Best Known (37−29, 37, s)-Nets in Base 64

(37−29, 37, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 37, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 37, 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]

(37−29, 37, 4225)-Net in Base 64 — Upper bound on s

There is no (8, 37, 4226)-net in base 64, because

1 times m-reduction [i] would yield (8, 36, 4226)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 105446 663214 199582 967252 455918 567961 658607 529787 713554 035552 600256 > 64³⁶ [i]