MinT - Best Known (144, 144+42, s)-Nets in Base 3

Best Known (144, 144+42, s)-Nets in Base 3

(144, 144+42, 600)-Net over F₃ — Constructive and digital

Digital (144, 186, 600)-net over F₃, using

3² times duplication [i] based on digital (142, 184, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 46, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(144, 144+42, 1199)-Net over F₃ — Digital

Digital (144, 186, 1199)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+42, 72991)-Net in Base 3 — Upper bound on s

There is no (144, 186, 72992)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55542 740060 133740 226957 125884 489092 946941 998715 664283 620440 535809 808384 801409 856366 906945 > 3¹⁸⁶ [i]