MinT - Best Known (234−116, 234, s)-Nets in Base 3

Best Known (234−116, 234, s)-Nets in Base 3

(234−116, 234, 76)-Net over F₃ — Constructive and digital

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]

(234−116, 234, 120)-Net over F₃ — Digital

Digital (118, 234, 120)-net over F₃, using

t-expansion [i] based on digital (113, 234, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(234−116, 234, 888)-Net in Base 3 — Upper bound on s

There is no (118, 234, 889)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4634 264156 628646 573398 295065 227754 361939 041633 350041 393845 050927 656609 265946 870754 681152 780367 296280 523184 842265 > 3²³⁴ [i]