MinT - Best Known (145−53, 145, s)-Nets in Base 3

Best Known (145−53, 145, s)-Nets in Base 3

(145−53, 145, 148)-Net over F₃ — Constructive and digital

Digital (92, 145, 148)-net over F₃, using

5 times m-reduction [i] based on digital (92, 150, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 75, 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]

(145−53, 145, 184)-Net over F₃ — Digital

Digital (92, 145, 184)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−53, 145, 2290)-Net in Base 3 — Upper bound on s

There is no (92, 145, 2291)-net in base 3, because

1 times m-reduction [i] would yield (92, 144, 2291)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 508 431154 029430 417755 164454 366682 289999 404395 169720 616090 348322 678165 > 3¹⁴⁴ [i]