MinT - Best Known (44, 77, s)-Nets in Base 5

Best Known (44, 77, s)-Nets in Base 5

(44, 77, 132)-Net over F₅ — Constructive and digital

Digital (44, 77, 132)-net over F₅, using

3 times m-reduction [i] based on digital (44, 80, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 40, 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]

(44, 77, 145)-Net over F₅ — Digital

Digital (44, 77, 145)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 77, 3541)-Net in Base 5 — Upper bound on s

There is no (44, 77, 3542)-net in base 5, because

1 times m-reduction [i] would yield (44, 76, 3542)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 132682 895856 946018 842092 563104 352042 063937 311998 437121 > 5⁷⁶ [i]