MinT - Best Known (96−37, 96, s)-Nets in Base 3

Best Known (96−37, 96, s)-Nets in Base 3

(96−37, 96, 80)-Net over F₃ — Constructive and digital

Digital (59, 96, 80)-net over F₃, using

6 times m-reduction [i] based on digital (59, 102, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 51, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(96−37, 96, 113)-Net over F₃ — Digital

Digital (59, 96, 113)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−37, 96, 1227)-Net in Base 3 — Upper bound on s

There is no (59, 96, 1228)-net in base 3, because

1 times m-reduction [i] would yield (59, 95, 1228)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2126 888909 857805 820498 029100 291510 508754 051817 > 3⁹⁵ [i]