MinT - Best Known (171, 226, s)-Nets in Base 3

Best Known (171, 226, s)-Nets in Base 3

(171, 226, 400)-Net over F₃ — Constructive and digital

Digital (171, 226, 400)-net over F₃, using

3² times duplication [i] based on digital (169, 224, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 56, 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]

(171, 226, 1046)-Net over F₃ — Digital

Digital (171, 226, 1046)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 226, 51661)-Net in Base 3 — Upper bound on s

There is no (171, 226, 51662)-net in base 3, because

1 times m-reduction [i] would yield (171, 225, 51662)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225144 784136 221267 646993 622796 524720 571647 859309 030093 264833 581872 554973 542860 576899 498269 755704 271747 515345 > 3²²⁵ [i]