MinT - Best Known (105−47, 105, s)-Nets in Base 5

Best Known (105−47, 105, s)-Nets in Base 5

(105−47, 105, 132)-Net over F₅ — Constructive and digital

Digital (58, 105, 132)-net over F₅, using

3 times m-reduction [i] based on digital (58, 108, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 54, 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]

(105−47, 105, 159)-Net over F₅ — Digital

Digital (58, 105, 159)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−47, 105, 3394)-Net in Base 5 — Upper bound on s

There is no (58, 105, 3395)-net in base 5, because

1 times m-reduction [i] would yield (58, 104, 3395)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 934855 702991 440530 240020 043048 300287 962353 281879 332751 341885 554166 526325 > 5¹⁰⁴ [i]