MinT - Best Known (206−85, 206, s)-Nets in Base 3

Best Known (206−85, 206, s)-Nets in Base 3

(206−85, 206, 148)-Net over F₃ — Constructive and digital

Digital (121, 206, 148)-net over F₃, using

2 times m-reduction [i] based on digital (121, 208, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 104, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(206−85, 206, 176)-Net over F₃ — Digital

Digital (121, 206, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−85, 206, 1719)-Net in Base 3 — Upper bound on s

There is no (121, 206, 1720)-net in base 3, because

1 times m-reduction [i] would yield (121, 205, 1720)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65 838459 512187 393420 863114 926814 270406 051928 540948 935121 895416 839536 892783 360609 233635 895287 329105 > 3²⁰⁵ [i]