MinT - Best Known (85−33, 85, s)-Nets in Base 5

Best Known (85−33, 85, s)-Nets in Base 5

(85−33, 85, 208)-Net over F₅ — Constructive and digital

Digital (52, 85, 208)-net over F₅, using

1 times m-reduction [i] based on digital (52, 86, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 43, 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]

(85−33, 85, 226)-Net over F₅ — Digital

Digital (52, 85, 226)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−33, 85, 7933)-Net in Base 5 — Upper bound on s

There is no (52, 85, 7934)-net in base 5, because

1 times m-reduction [i] would yield (52, 84, 7934)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 51793 431546 445339 699698 599289 562393 357042 042164 616382 514945 > 5⁸⁴ [i]