MinT - Best Known (207−45, 207, s)-Nets in Base 3

Best Known (207−45, 207, s)-Nets in Base 3

(207−45, 207, 640)-Net over F₃ — Constructive and digital

Digital (162, 207, 640)-net over F₃, using

t-expansion [i] based on digital (161, 207, 640)-net over F₃, using
- 1 times m-reduction [i] based on digital (161, 208, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 52, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(207−45, 207, 1537)-Net over F₃ — Digital

Digital (162, 207, 1537)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−45, 207, 132844)-Net in Base 3 — Upper bound on s

There is no (162, 207, 132845)-net in base 3, because

1 times m-reduction [i] would yield (162, 206, 132845)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 657399 036210 717697 464918 543765 745380 247475 051439 592694 155859 302677 784251 655887 474571 044193 623953 > 3²⁰⁶ [i]