MinT - Best Known (229−50, 229, s)-Nets in Base 3

Best Known (229−50, 229, s)-Nets in Base 3

(229−50, 229, 688)-Net over F₃ — Constructive and digital

Digital (179, 229, 688)-net over F₃, using

3¹ times duplication [i] based on digital (178, 228, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 57, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(229−50, 229, 1646)-Net over F₃ — Digital

Digital (179, 229, 1646)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−50, 229, 119381)-Net in Base 3 — Upper bound on s

There is no (179, 229, 119382)-net in base 3, because

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]