MinT - Best Known (171, 171+53, s)-Nets in Base 3

Best Known (171, 171+53, s)-Nets in Base 3

(171, 171+53, 464)-Net over F₃ — Constructive and digital

Digital (171, 224, 464)-net over F₃, using

t-expansion [i] based on digital (170, 224, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 56, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(171, 171+53, 1166)-Net over F₃ — Digital

Digital (171, 224, 1166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+53, 65211)-Net in Base 3 — Upper bound on s

There is no (171, 224, 65212)-net in base 3, because

1 times m-reduction [i] would yield (171, 223, 65212)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25008 646957 667916 839270 998448 364265 901867 641929 623342 577173 813315 261381 816398 248746 947027 915507 198774 175625 > 3²²³ [i]