MinT - Best Known (209−91, 209, s)-Nets in Base 3

Best Known (209−91, 209, s)-Nets in Base 3

(209−91, 209, 128)-Net over F₃ — Constructive and digital

Digital (118, 209, 128)-net over F₃, using

1 times m-reduction [i] based on digital (118, 210, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 105, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(209−91, 209, 153)-Net over F₃ — Digital

Digital (118, 209, 153)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−91, 209, 1370)-Net in Base 3 — Upper bound on s

There is no (118, 209, 1371)-net in base 3, because

1 times m-reduction [i] would yield (118, 208, 1371)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1784 657706 443209 230156 981685 152707 191063 694966 947174 446008 892036 275612 909866 020073 110795 244841 958751 > 3²⁰⁸ [i]