MinT - Best Known (71−27, 71, s)-Nets in Base 5

Best Known (71−27, 71, s)-Nets in Base 5

(71−27, 71, 132)-Net over F₅ — Constructive and digital

Digital (44, 71, 132)-net over F₅, using

9 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]

(71−27, 71, 216)-Net over F₅ — Digital

Digital (44, 71, 216)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−27, 71, 8213)-Net in Base 5 — Upper bound on s

There is no (44, 71, 8214)-net in base 5, because

1 times m-reduction [i] would yield (44, 70, 8214)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8 473490 968852 515237 858724 304001 077088 047790 809049 > 5⁷⁰ [i]