MinT - Best Known (86−25, 86, s)-Nets in Base 3

Best Known (86−25, 86, s)-Nets in Base 3

(86−25, 86, 156)-Net over F₃ — Constructive and digital

Digital (61, 86, 156)-net over F₃, using

1 times m-reduction [i] based on digital (61, 87, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 29, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(86−25, 86, 255)-Net over F₃ — Digital

Digital (61, 86, 255)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−25, 86, 6326)-Net in Base 3 — Upper bound on s

There is no (61, 86, 6327)-net in base 3, because

1 times m-reduction [i] would yield (61, 85, 6327)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35962 819458 941614 797934 123584 043948 462569 > 3⁸⁵ [i]