MinT - Best Known (58−21, 58, s)-Nets in Base 5

Best Known (58−21, 58, s)-Nets in Base 5

(58−21, 58, 132)-Net over F₅ — Constructive and digital

Digital (37, 58, 132)-net over F₅, using

8 times m-reduction [i] based on digital (37, 66, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 33, 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]

(58−21, 58, 231)-Net over F₅ — Digital

Digital (37, 58, 231)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58−21, 58, 10908)-Net in Base 5 — Upper bound on s

There is no (37, 58, 10909)-net in base 5, because

1 times m-reduction [i] would yield (37, 57, 10909)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6941 790259 725084 633340 211683 874080 067065 > 5⁵⁷ [i]