MinT - Best Known (40, 61, s)-Nets in Base 5

Best Known (40, 61, s)-Nets in Base 5

(40, 61, 208)-Net over F₅ — Constructive and digital

Digital (40, 61, 208)-net over F₅, using

1 times m-reduction [i] based on digital (40, 62, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 31, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(40, 61, 291)-Net over F₅ — Digital

Digital (40, 61, 291)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 61, 17683)-Net in Base 5 — Upper bound on s

There is no (40, 61, 17684)-net in base 5, because

1 times m-reduction [i] would yield (40, 60, 17684)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 867681 730092 539261 481244 775924 964613 306305 > 5⁶⁰ [i]