MinT - Best Known (60, 111, s)-Nets in Base 5

Best Known (60, 111, s)-Nets in Base 5

(60, 111, 132)-Net over F₅ — Constructive and digital

Digital (60, 111, 132)-net over F₅, using

1 times m-reduction [i] based on digital (60, 112, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 56, 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]

(60, 111, 151)-Net over F₅ — Digital

Digital (60, 111, 151)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 111, 3008)-Net in Base 5 — Upper bound on s

There is no (60, 111, 3009)-net in base 5, because

1 times m-reduction [i] would yield (60, 110, 3009)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77076 119921 488011 723289 014341 634879 220566 893645 517587 756121 910625 873420 186405 > 5¹¹⁰ [i]