MinT - Best Known (38, 38+21, s)-Nets in Base 5

Best Known (38, 38+21, s)-Nets in Base 5

(38, 38+21, 132)-Net over F₅ — Constructive and digital

Digital (38, 59, 132)-net over F₅, using

9 times m-reduction [i] based on digital (38, 68, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 34, 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]

(38, 38+21, 249)-Net over F₅ — Digital

Digital (38, 59, 249)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+21, 12814)-Net in Base 5 — Upper bound on s

There is no (38, 59, 12815)-net in base 5, because

1 times m-reduction [i] would yield (38, 58, 12815)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 34705 165960 810456 449800 250697 377982 049241 > 5⁵⁸ [i]