MinT - Best Known (145−55, 145, s)-Nets in Base 3

Best Known (145−55, 145, s)-Nets in Base 3

(145−55, 145, 148)-Net over F₃ — Constructive and digital

Digital (90, 145, 148)-net over F₃, using

1 times m-reduction [i] based on digital (90, 146, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 73, 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]

(145−55, 145, 165)-Net over F₃ — Digital

Digital (90, 145, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−55, 145, 1888)-Net in Base 3 — Upper bound on s

There is no (90, 145, 1889)-net in base 3, because

1 times m-reduction [i] would yield (90, 144, 1889)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 514 652614 907911 722803 149521 822488 514215 590657 685375 038173 677588 158011 > 3¹⁴⁴ [i]