MinT - Best Known (51−41, 51, s)-Nets in Base 64

Best Known (51−41, 51, s)-Nets in Base 64

(51−41, 51, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 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]

(51−41, 51, 225)-Net over F₆₄ — Digital

Digital (10, 51, 225)-net over F₆₄, using

net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
  - a curve from the manYPoints database [i]

(51−41, 51, 4309)-Net in Base 64 — Upper bound on s

There is no (10, 51, 4310)-net in base 64, because

1 times m-reduction [i] would yield (10, 50, 4310)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 041667 990905 225406 778040 001607 728521 778483 041560 655666 071081 263044 482380 792772 110395 151929 > 64⁵⁰ [i]