MinT - Best Known (160, 160+46, s)-Nets in Base 3

Best Known (160, 160+46, s)-Nets in Base 3

(160, 160+46, 640)-Net over F₃ — Constructive and digital

Digital (160, 206, 640)-net over F₃, using

3² times duplication [i] based on digital (158, 204, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 51, 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]

(160, 160+46, 1369)-Net over F₃ — Digital

Digital (160, 206, 1369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+46, 88442)-Net in Base 3 — Upper bound on s

There is no (160, 206, 88443)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 640296 952360 352084 847655 230266 236501 093973 816188 719743 652313 519379 791210 853980 703925 032881 171523 > 3²⁰⁶ [i]