MinT - Best Known (6, 44, s)-Nets in Base 64

Best Known (6, 44, s)-Nets in Base 64

(6, 44, 128)-Net over F₆₄ — Constructive and digital

Digital (6, 44, 128)-net over F₆₄, using

t-expansion [i] based on digital (5, 44, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(6, 44, 161)-Net over F₆₄ — Digital

Digital (6, 44, 161)-net over F₆₄, using

net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(6, 44, 1907)-Net in Base 64 — Upper bound on s

There is no (6, 44, 1908)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 29 747754 004668 361677 857938 534082 179625 022303 771529 164636 946751 172342 084673 608613 > 64⁴⁴ [i]