MinT - Best Known (54−19, 54, s)-Nets in Base 5

Best Known (54−19, 54, s)-Nets in Base 5

(54−19, 54, 132)-Net over F₅ — Constructive and digital

Digital (35, 54, 132)-net over F₅, using

8 times m-reduction [i] based on digital (35, 62, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 31, 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]

(54−19, 54, 245)-Net over F₅ — Digital

Digital (35, 54, 245)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−19, 54, 13540)-Net in Base 5 — Upper bound on s

There is no (35, 54, 13541)-net in base 5, because

1 times m-reduction [i] would yield (35, 53, 13541)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11 102911 712174 661075 402715 547198 925045 > 5⁵³ [i]