MinT - Best Known (174, 245, s)-Nets in Base 3

Best Known (174, 245, s)-Nets in Base 3

(174, 245, 282)-Net over F₃ — Constructive and digital

Digital (174, 245, 282)-net over F₃, using

1 times m-reduction [i] based on digital (174, 246, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 82, 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]

(174, 245, 592)-Net over F₃ — Digital

Digital (174, 245, 592)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 245, 14703)-Net in Base 3 — Upper bound on s

There is no (174, 245, 14704)-net in base 3, because

1 times m-reduction [i] would yield (174, 244, 14704)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 261 605850 927879 361233 947207 416896 189384 118032 555687 160802 881060 296837 093370 185554 346990 518166 180599 147266 781479 647681 > 3²⁴⁴ [i]