MinT - Best Known (198−92, 198, s)-Nets in Base 3

Best Known (198−92, 198, s)-Nets in Base 3

(198−92, 198, 76)-Net over F₃ — Constructive and digital

Digital (106, 198, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 61, 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, 137, 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]

(198−92, 198, 122)-Net over F₃ — Digital

Digital (106, 198, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−92, 198, 973)-Net in Base 3 — Upper bound on s

There is no (106, 198, 974)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29950 265071 552422 110497 447598 765698 565603 431282 555073 743889 681347 994925 435361 708915 268676 336981 > 3¹⁹⁸ [i]