MinT - Best Known (10, 10+50, s)-Nets in Base 64

Best Known (10, 10+50, s)-Nets in Base 64

(10, 10+50, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 60, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 60, 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]

(10, 10+50, 225)-Net over F₆₄ — Digital

Digital (10, 60, 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]

(10, 10+50, 3479)-Net in Base 64 — Upper bound on s

There is no (10, 60, 3480)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 349255 409495 720057 147113 870158 663763 969103 740055 550791 909411 204025 886863 387413 937177 918945 260205 398503 730576 > 64⁶⁰ [i]