MinT - Best Known (83−33, 83, s)-Nets in Base 5

Best Known (83−33, 83, s)-Nets in Base 5

(83−33, 83, 132)-Net over F₅ — Constructive and digital

Digital (50, 83, 132)-net over F₅, using

9 times m-reduction [i] based on digital (50, 92, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 46, 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]

(83−33, 83, 202)-Net over F₅ — Digital

Digital (50, 83, 202)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−33, 83, 6485)-Net in Base 5 — Upper bound on s

There is no (50, 83, 6486)-net in base 5, because

1 times m-reduction [i] would yield (50, 82, 6486)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2071 442888 018712 670817 174087 281512 508812 088386 536029 972225 > 5⁸² [i]