MinT - Best Known (112, 112+105, s)-Nets in Base 3

Best Known (112, 112+105, s)-Nets in Base 3

(112, 112+105, 76)-Net over F₃ — Constructive and digital

Digital (112, 217, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 67, 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, 150, 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]

(112, 112+105, 118)-Net over F₃ — Digital

Digital (112, 217, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+105, 919)-Net in Base 3 — Upper bound on s

There is no (112, 217, 920)-net in base 3, because

1 times m-reduction [i] would yield (112, 216, 920)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 699813 740615 125002 476981 666212 756296 913376 671532 965902 807933 101476 547135 956901 034466 066570 332444 131521 > 3²¹⁶ [i]