MinT - Best Known (207−89, 207, s)-Nets in Base 3

Best Known (207−89, 207, s)-Nets in Base 3

(207−89, 207, 128)-Net over F₃ — Constructive and digital

Digital (118, 207, 128)-net over F₃, using

3 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]

(207−89, 207, 157)-Net over F₃ — Digital

Digital (118, 207, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−89, 207, 1435)-Net in Base 3 — Upper bound on s

There is no (118, 207, 1436)-net in base 3, because

1 times m-reduction [i] would yield (118, 206, 1436)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199 063570 379848 163203 088551 479163 025563 705845 965653 161158 635957 500497 748571 141480 885575 313680 838977 > 3²⁰⁶ [i]