MinT - Best Known (129, 222, s)-Nets in Base 3

Best Known (129, 222, s)-Nets in Base 3

(129, 222, 148)-Net over F₃ — Constructive and digital

Digital (129, 222, 148)-net over F₃, using

2 times m-reduction [i] based on digital (129, 224, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 112, 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]

(129, 222, 180)-Net over F₃ — Digital

Digital (129, 222, 180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 222, 1718)-Net in Base 3 — Upper bound on s

There is no (129, 222, 1719)-net in base 3, because

1 times m-reduction [i] would yield (129, 221, 1719)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2792 150640 410074 070654 723182 886582 734816 958310 222406 062715 677823 661078 004020 500720 746423 215838 964272 144213 > 3²²¹ [i]