MinT - Best Known (172, 227, s)-Nets in Base 3

Best Known (172, 227, s)-Nets in Base 3

(172, 227, 400)-Net over F₃ — Constructive and digital

Digital (172, 227, 400)-net over F₃, using

1 times m-reduction [i] based on digital (172, 228, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 57, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(172, 227, 1069)-Net over F₃ — Digital

Digital (172, 227, 1069)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 227, 53807)-Net in Base 3 — Upper bound on s

There is no (172, 227, 53808)-net in base 3, because

1 times m-reduction [i] would yield (172, 226, 53808)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 675249 648917 285141 891682 706719 912188 681793 020260 140912 980519 618485 012551 544890 827424 069372 422998 230316 883649 > 3²²⁶ [i]