MinT - Best Known (206−93, 206, s)-Nets in Base 3

Best Known (206−93, 206, s)-Nets in Base 3

(206−93, 206, 80)-Net over F₃ — Constructive and digital

Digital (113, 206, 80)-net over F₃, using

4 times m-reduction [i] based on digital (113, 210, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 105, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(206−93, 206, 137)-Net over F₃ — Digital

Digital (113, 206, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−93, 206, 1158)-Net in Base 3 — Upper bound on s

There is no (113, 206, 1159)-net in base 3, because

1 times m-reduction [i] would yield (113, 205, 1159)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 902543 756909 583629 891648 940511 027543 952938 682216 010661 711576 667398 905823 684766 462744 223888 355445 > 3²⁰⁵ [i]