MinT - Best Known (38, 38+27, s)-Nets in Base 5

Best Known (38, 38+27, s)-Nets in Base 5

(38, 38+27, 132)-Net over F₅ — Constructive and digital

Digital (38, 65, 132)-net over F₅, using

3 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+27, 144)-Net over F₅ — Digital

Digital (38, 65, 144)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+27, 3903)-Net in Base 5 — Upper bound on s

There is no (38, 65, 3904)-net in base 5, because

1 times m-reduction [i] would yield (38, 64, 3904)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 543 846999 656526 213797 177114 641573 275091 883265 > 5⁶⁴ [i]