MinT - Best Known (199−120, 199, s)-Nets in Base 3

Best Known (199−120, 199, s)-Nets in Base 3

(199−120, 199, 54)-Net over F₃ — Constructive and digital

Digital (79, 199, 54)-net over F₃, using

net from sequence [i] based on digital (79, 53)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 53)-sequence over F₉, using
  - s-reduction based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(199−120, 199, 84)-Net over F₃ — Digital

Digital (79, 199, 84)-net over F₃, using

t-expansion [i] based on digital (71, 199, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(199−120, 199, 386)-Net in Base 3 — Upper bound on s

There is no (79, 199, 387)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88980 221583 728725 557682 927200 732443 249853 773666 454904 914504 640403 203039 134567 277630 376112 604393 > 3¹⁹⁹ [i]