MinT - Best Known (230−51, 230, s)-Nets in Base 3

Best Known (230−51, 230, s)-Nets in Base 3

(230−51, 230, 640)-Net over F₃ — Constructive and digital

Digital (179, 230, 640)-net over F₃, using

2 times m-reduction [i] based on digital (179, 232, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 58, 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]

(230−51, 230, 1550)-Net over F₃ — Digital

Digital (179, 230, 1550)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−51, 230, 119381)-Net in Base 3 — Upper bound on s

There is no (179, 230, 119382)-net in base 3, because

1 times m-reduction [i] would yield (179, 229, 119382)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 230695 522613 743908 218199 938319 984305 370902 941343 494912 840249 360681 182501 996095 123134 505439 713104 104341 485053 > 3²²⁹ [i]