MinT - Best Known (144, 144+103, s)-Nets in Base 3

Best Known (144, 144+103, s)-Nets in Base 3

(144, 144+103, 148)-Net over F₃ — Constructive and digital

Digital (144, 247, 148)-net over F₃, using

t-expansion [i] based on digital (142, 247, 148)-net over F₃, using
- 3 times m-reduction [i] based on digital (142, 250, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 125, 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]

(144, 144+103, 200)-Net over F₃ — Digital

Digital (144, 247, 200)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+103, 1937)-Net in Base 3 — Upper bound on s

There is no (144, 247, 1938)-net in base 3, because

1 times m-reduction [i] would yield (144, 246, 1938)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2403 313120 612429 064509 335829 491329 438631 152800 595264 897497 329797 131058 657637 517212 845043 382450 906286 162725 648917 705009 > 3²⁴⁶ [i]