MinT - Best Known (220−106, 220, s)-Nets in Base 3

Best Known (220−106, 220, s)-Nets in Base 3

(220−106, 220, 76)-Net over F₃ — Constructive and digital

Digital (114, 220, 76)-net over F₃, using

2 times m-reduction [i] based on digital (114, 222, 76)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 69, 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, 153, 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]

(220−106, 220, 121)-Net over F₃ — Digital

Digital (114, 220, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−106, 220, 933)-Net in Base 3 — Upper bound on s

There is no (114, 220, 934)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 964 618310 626946 893108 369366 488283 909211 810784 821141 542306 830952 741081 152766 765216 767046 318480 092608 516805 > 3²²⁰ [i]