MinT - Best Known (79−35, 79, s)-Nets in Base 5

Best Known (79−35, 79, s)-Nets in Base 5

(79−35, 79, 132)-Net over F₅ — Constructive and digital

Digital (44, 79, 132)-net over F₅, using

1 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]

(79−35, 79, 2877)-Net in Base 5 — Upper bound on s

There is no (44, 79, 2878)-net in base 5, because

1 times m-reduction [i] would yield (44, 78, 2878)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 309826 536740 660073 863514 455602 370090 909881 545647 871225 > 5⁷⁸ [i]