MinT - Best Known (197−56, 197, s)-Nets in Base 3

Best Known (197−56, 197, s)-Nets in Base 3

(197−56, 197, 264)-Net over F₃ — Constructive and digital

Digital (141, 197, 264)-net over F₃, using

1 times m-reduction [i] based on digital (141, 198, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 66, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(197−56, 197, 523)-Net over F₃ — Digital

Digital (141, 197, 523)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−56, 197, 12821)-Net in Base 3 — Upper bound on s

There is no (141, 197, 12822)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9851 224266 568737 349500 633564 569598 545517 383058 352216 015059 376798 943505 618771 833984 373467 090937 > 3¹⁹⁷ [i]