MinT - Best Known (206−50, 206, s)-Nets in Base 3

Best Known (206−50, 206, s)-Nets in Base 3

(206−50, 206, 400)-Net over F₃ — Constructive and digital

Digital (156, 206, 400)-net over F₃, using

3² times duplication [i] based on digital (154, 204, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 51, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(206−50, 206, 980)-Net over F₃ — Digital

Digital (156, 206, 980)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−50, 206, 43434)-Net in Base 3 — Upper bound on s

There is no (156, 206, 43435)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 740718 990761 247613 798853 231128 404310 106451 538023 842259 306912 341415 082692 164015 565700 451218 415207 > 3²⁰⁶ [i]