MinT - Best Known (108, 173, s)-Nets in Base 3

Best Known (108, 173, s)-Nets in Base 3

(108, 173, 148)-Net over F₃ — Constructive and digital

Digital (108, 173, 148)-net over F₃, using

9 times m-reduction [i] based on digital (108, 182, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 91, 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]

(108, 173, 197)-Net over F₃ — Digital

Digital (108, 173, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 173, 2314)-Net in Base 3 — Upper bound on s

There is no (108, 173, 2315)-net in base 3, because

1 times m-reduction [i] would yield (108, 172, 2315)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11620 029990 477950 460779 741217 489256 577340 192240 409674 027482 358892 874462 696641 692609 > 3¹⁷² [i]