MinT - Best Known (120, 205, s)-Nets in Base 3

Best Known (120, 205, s)-Nets in Base 3

(120, 205, 148)-Net over F₃ — Constructive and digital

Digital (120, 205, 148)-net over F₃, using

1 times m-reduction [i] based on digital (120, 206, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 103, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(120, 205, 173)-Net over F₃ — Digital

Digital (120, 205, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 205, 1673)-Net in Base 3 — Upper bound on s

There is no (120, 205, 1674)-net in base 3, because

1 times m-reduction [i] would yield (120, 204, 1674)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 656759 632134 521531 715664 702486 674654 039555 376403 297450 178420 944390 079779 871268 971207 518535 115925 > 3²⁰⁴ [i]