MinT - Best Known (90−79, 90, s)-Nets in Base 64

Best Known (90−79, 90, s)-Nets in Base 64

(90−79, 90, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 90, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 90, 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]

(90−79, 90, 225)-Net over F₆₄ — Digital

Digital (11, 90, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 90, 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]

(90−79, 90, 3215)-Net in Base 64 — Upper bound on s

There is no (11, 90, 3216)-net in base 64, because

1 times m-reduction [i] would yield (11, 89, 3216)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56612 532648 111814 288838 091826 780375 805995 153093 687712 373806 649660 316870 674565 114165 777264 893671 504464 688580 561027 516917 254877 970941 032167 791716 894630 654880 245180 > 64⁸⁹ [i]