MinT - Best Known (66−25, 66, s)-Nets in Base 5

Best Known (66−25, 66, s)-Nets in Base 5

(66−25, 66, 132)-Net over F₅ — Constructive and digital

Digital (41, 66, 132)-net over F₅, using

8 times m-reduction [i] based on digital (41, 74, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 37, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(66−25, 66, 210)-Net over F₅ — Digital

Digital (41, 66, 210)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66−25, 66, 8071)-Net in Base 5 — Upper bound on s

There is no (41, 66, 8072)-net in base 5, because

1 times m-reduction [i] would yield (41, 65, 8072)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2714 186126 744086 093535 669495 659424 353633 465345 > 5⁶⁵ [i]