MinT - Best Known (239−69, 239, s)-Nets in Base 3

Best Known (239−69, 239, s)-Nets in Base 3

(239−69, 239, 282)-Net over F₃ — Constructive and digital

Digital (170, 239, 282)-net over F₃, using

1 times m-reduction [i] based on digital (170, 240, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 80, 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]

(239−69, 239, 587)-Net over F₃ — Digital

Digital (170, 239, 587)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−69, 239, 14767)-Net in Base 3 — Upper bound on s

There is no (170, 239, 14768)-net in base 3, because

1 times m-reduction [i] would yield (170, 238, 14768)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 359102 551239 476329 274268 169998 255507 626107 812082 430019 823903 786974 724170 372445 884761 153781 745208 961530 235234 263073 > 3²³⁸ [i]