MinT - Best Known (59−21, 59, s)-Nets in Base 3

Best Known (59−21, 59, s)-Nets in Base 3

(59−21, 59, 80)-Net over F₃ — Constructive and digital

Digital (38, 59, 80)-net over F₃, using

1 times m-reduction [i] based on digital (38, 60, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 30, 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]

(59−21, 59, 101)-Net over F₃ — Digital

Digital (38, 59, 101)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−21, 59, 1315)-Net in Base 3 — Upper bound on s

There is no (38, 59, 1316)-net in base 3, because

1 times m-reduction [i] would yield (38, 58, 1316)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4723 250217 414861 422513 503097 > 3⁵⁸ [i]