MinT - Best Known (109−35, 109, s)-Nets in Base 3

Best Known (109−35, 109, s)-Nets in Base 3

(109−35, 109, 148)-Net over F₃ — Constructive and digital

Digital (74, 109, 148)-net over F₃, using

5 times m-reduction [i] based on digital (74, 114, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 57, 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]

(109−35, 109, 216)-Net over F₃ — Digital

Digital (74, 109, 216)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−35, 109, 3838)-Net in Base 3 — Upper bound on s

There is no (74, 109, 3839)-net in base 3, because

1 times m-reduction [i] would yield (74, 108, 3839)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3386 545752 345644 183750 286514 190351 335104 959401 336287 > 3¹⁰⁸ [i]