MinT - Best Known (69−25, 69, s)-Nets in Base 5

Best Known (69−25, 69, s)-Nets in Base 5

(69−25, 69, 208)-Net over F₅ — Constructive and digital

Digital (44, 69, 208)-net over F₅, using

1 times m-reduction [i] based on digital (44, 70, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 35, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(69−25, 69, 261)-Net over F₅ — Digital

Digital (44, 69, 261)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(69−25, 69, 12073)-Net in Base 5 — Upper bound on s

There is no (44, 69, 12074)-net in base 5, because

1 times m-reduction [i] would yield (44, 68, 12074)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 339049 906462 003966 961028 418455 465637 876695 860673 > 5⁶⁸ [i]