MinT - Best Known (110, 209, s)-Nets in Base 3

Best Known (110, 209, s)-Nets in Base 3

(110, 209, 76)-Net over F₃ — Constructive and digital

Digital (110, 209, 76)-net over F₃, using

1 times m-reduction [i] based on digital (110, 210, 76)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 65, 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, 145, 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]

(110, 209, 121)-Net over F₃ — Digital

Digital (110, 209, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 209, 965)-Net in Base 3 — Upper bound on s

There is no (110, 209, 966)-net in base 3, because

1 times m-reduction [i] would yield (110, 208, 966)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1790 284077 689207 186909 863298 648529 671011 414642 486995 525229 791749 659167 249823 738199 063375 093045 098797 > 3²⁰⁸ [i]