MinT - Best Known (143−36, 143, s)-Nets in Base 3

Best Known (143−36, 143, s)-Nets in Base 3

(143−36, 143, 288)-Net over F₃ — Constructive and digital

Digital (107, 143, 288)-net over F₃, using

1 times m-reduction [i] based on digital (107, 144, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 48, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(143−36, 143, 636)-Net over F₃ — Digital

Digital (107, 143, 636)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−36, 143, 23293)-Net in Base 3 — Upper bound on s

There is no (107, 143, 23294)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 223630 897547 466139 957519 344483 128917 028754 611352 511257 469082 684445 > 3¹⁴³ [i]