MinT - Best Known (143, 143+66, s)-Nets in Base 3

Best Known (143, 143+66, s)-Nets in Base 3

(143, 143+66, 167)-Net over F₃ — Constructive and digital

Digital (143, 209, 167)-net over F₃, using

1 times m-reduction [i] based on digital (143, 210, 167)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 42, 19)-net over F₃, using
    - net from sequence [i] based on digital (9, 18)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
        an explicitly constructive algebraic function field [i]
  2. digital (101, 168, 148)-net over F₃, using
    - trace code for nets [i] based on digital (17, 84, 74)-net over F₉, using
      - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
        a function field by GarcÃa and Quoos [i]

(143, 143+66, 393)-Net over F₃ — Digital

Digital (143, 209, 393)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+66, 6887)-Net in Base 3 — Upper bound on s

There is no (143, 209, 6888)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5244 560058 310381 268594 426932 917149 172181 611050 332396 968240 965282 344492 950261 736182 754981 713502 496721 > 3²⁰⁹ [i]