MinT - Best Known (143−39, 143, s)-Nets in Base 3

Best Known (143−39, 143, s)-Nets in Base 3

(143−39, 143, 252)-Net over F₃ — Constructive and digital

Digital (104, 143, 252)-net over F₃, using

1 times m-reduction [i] based on digital (104, 144, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 48, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(143−39, 143, 466)-Net over F₃ — Digital

Digital (104, 143, 466)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−39, 143, 14570)-Net in Base 3 — Upper bound on s

There is no (104, 143, 14571)-net in base 3, because

1 times m-reduction [i] would yield (104, 142, 14571)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 394598 040306 088074 720113 060182 418583 982805 717365 211588 817686 249131 > 3¹⁴² [i]