MinT - Best Known (140−74, 140, s)-Nets in Base 3

Best Known (140−74, 140, s)-Nets in Base 3

(140−74, 140, 52)-Net over F₃ — Constructive and digital

Digital (66, 140, 52)-net over F₃, using

2 times m-reduction [i] based on digital (66, 142, 52)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 51, 24)-net over F₃, using
    - net from sequence [i] based on digital (13, 23)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
  2. digital (15, 91, 28)-net over F₃, using
    - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
        an explicitly constructive algebraic function field [i]

(140−74, 140, 64)-Net over F₃ — Digital

Digital (66, 140, 64)-net over F₃, using

t-expansion [i] based on digital (49, 140, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(140−74, 140, 432)-Net in Base 3 — Upper bound on s

There is no (66, 140, 433)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 469450 710638 564573 154462 740708 983937 987988 376188 052312 411267 866579 > 3¹⁴⁰ [i]