MinT - Best Known (118, 161, s)-Nets in Base 3

Best Known (118, 161, s)-Nets in Base 3

(118, 161, 282)-Net over F₃ — Constructive and digital

Digital (118, 161, 282)-net over F₃, using

1 times m-reduction [i] based on digital (118, 162, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 54, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(118, 161, 553)-Net over F₃ — Digital

Digital (118, 161, 553)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 161, 18715)-Net in Base 3 — Upper bound on s

There is no (118, 161, 18716)-net in base 3, because

1 times m-reduction [i] would yield (118, 160, 18716)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21864 484768 762698 917457 247323 181378 149160 539868 303604 882951 744671 932323 803929 > 3¹⁶⁰ [i]