MinT - Best Known (74, 74+67, s)-Nets in Base 3

Best Known (74, 74+67, s)-Nets in Base 3

(74, 74+67, 64)-Net over F₃ — Constructive and digital

Digital (74, 141, 64)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 48, 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]
2. digital (26, 93, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]

(74, 74+67, 86)-Net over F₃ — Digital

Digital (74, 141, 86)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+67, 663)-Net in Base 3 — Upper bound on s

There is no (74, 141, 664)-net in base 3, because

1 times m-reduction [i] would yield (74, 140, 664)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 294747 349380 278276 270204 414079 023346 161508 082870 724939 230254 123825 > 3¹⁴⁰ [i]