MinT - Best Known (111, 214, s)-Nets in Base 3

Best Known (111, 214, s)-Nets in Base 3

(111, 214, 76)-Net over F₃ — Constructive and digital

Digital (111, 214, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 66, 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, 148, 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]

(111, 214, 118)-Net over F₃ — Digital

Digital (111, 214, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 214, 926)-Net in Base 3 — Upper bound on s

There is no (111, 214, 927)-net in base 3, because

1 times m-reduction [i] would yield (111, 213, 927)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 430357 049699 366815 538018 873814 231405 608075 734059 046931 081965 156339 755183 183009 650976 024677 663220 139035 > 3²¹³ [i]