MinT - Best Known (224−106, 224, s)-Nets in Base 3

Best Known (224−106, 224, s)-Nets in Base 3

(224−106, 224, 78)-Net over F₃ — Constructive and digital

Digital (118, 224, 78)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 79, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]
2. digital (39, 145, 42)-net over F₃, using
  - net from sequence [i] based on digital (39, 41)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(224−106, 224, 129)-Net over F₃ — Digital

Digital (118, 224, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−106, 224, 1018)-Net in Base 3 — Upper bound on s

There is no (118, 224, 1019)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77764 279609 107802 523898 120648 126090 393795 384848 257536 584200 831560 672109 217200 699974 888732 907488 045651 403215 > 3²²⁴ [i]