MinT - Best Known (118, 118+111, s)-Nets in Base 3

Best Known (118, 118+111, s)-Nets in Base 3

(118, 118+111, 76)-Net over F₃ — Constructive and digital

Digital (118, 229, 76)-net over F₃, using

5 times m-reduction [i] based on digital (118, 234, 76)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 73, 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 (45, 161, 48)-net over F₃, using
    - net from sequence [i] based on digital (45, 47)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
        an explicitly constructive algebraic function field [i]

(118, 118+111, 123)-Net over F₃ — Digital

Digital (118, 229, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+111, 960)-Net in Base 3 — Upper bound on s

There is no (118, 229, 961)-net in base 3, because

1 times m-reduction [i] would yield (118, 228, 961)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 200885 742253 126837 182648 816236 178535 732411 927310 590231 057233 332461 796526 133048 272420 580623 552716 471437 252299 > 3²²⁸ [i]