MinT - Best Known (143−60, 143, s)-Nets in Base 3

Best Known (143−60, 143, s)-Nets in Base 3

(143−60, 143, 80)-Net over F₃ — Constructive and digital

Digital (83, 143, 80)-net over F₃, using

7 times m-reduction [i] based on digital (83, 150, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 75, 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]

(143−60, 143, 123)-Net over F₃ — Digital

Digital (83, 143, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−60, 143, 1103)-Net in Base 3 — Upper bound on s

There is no (83, 143, 1104)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 172 285591 160056 397446 031415 072859 119398 204727 670149 578983 420982 822113 > 3¹⁴³ [i]