MinT - Best Known (206−63, 206, s)-Nets in Base 3

Best Known (206−63, 206, s)-Nets in Base 3

(206−63, 206, 204)-Net over F₃ — Constructive and digital

Digital (143, 206, 204)-net over F₃, using

1 times m-reduction [i] based on digital (143, 207, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 69, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(206−63, 206, 428)-Net over F₃ — Digital

Digital (143, 206, 428)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−63, 206, 8844)-Net in Base 3 — Upper bound on s

There is no (143, 206, 8845)-net in base 3, because

1 times m-reduction [i] would yield (143, 205, 8845)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 687365 460943 812010 843405 579793 942946 437521 694470 818998 033163 071006 043472 444116 166271 100622 003931 > 3²⁰⁵ [i]