MinT - Best Known (11, 11+56, s)-Nets in Base 64

Best Known (11, 11+56, s)-Nets in Base 64

(11, 11+56, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 67, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 67, 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]

(11, 11+56, 225)-Net over F₆₄ — Digital

Digital (11, 67, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 67, 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]

(11, 11+56, 3749)-Net in Base 64 — Upper bound on s

There is no (11, 67, 3750)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 10 360269 907426 945554 661035 667717 712664 707649 272808 983933 499653 999737 089553 408208 783400 762179 993094 959956 350786 848254 437076 > 64⁶⁷ [i]