MinT - Best Known (74−31, 74, s)-Nets in Base 5

Best Known (74−31, 74, s)-Nets in Base 5

(74−31, 74, 132)-Net over F₅ — Constructive and digital

Digital (43, 74, 132)-net over F₅, using

4 times m-reduction [i] based on digital (43, 78, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 39, 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]

(74−31, 74, 153)-Net over F₅ — Digital

Digital (43, 74, 153)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−31, 74, 4038)-Net in Base 5 — Upper bound on s

There is no (43, 74, 4039)-net in base 5, because

1 times m-reduction [i] would yield (43, 73, 4039)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1061 223235 219668 696995 362231 006477 456452 804411 844965 > 5⁷³ [i]