MinT - Best Known (185, 185+54, s)-Nets in Base 3

Best Known (185, 185+54, s)-Nets in Base 3

(185, 185+54, 640)-Net over F₃ — Constructive and digital

Digital (185, 239, 640)-net over F₃, using

1 times m-reduction [i] based on digital (185, 240, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 60, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(185, 185+54, 1486)-Net over F₃ — Digital

Digital (185, 239, 1486)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185, 185+54, 91339)-Net in Base 3 — Upper bound on s

There is no (185, 239, 91340)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 076652 050471 582488 563360 014836 210886 265128 096201 046401 998820 065833 739072 504552 285358 239689 050939 175365 023361 569169 > 3²³⁹ [i]