MinT - Best Known (75, 75+45, s)-Nets in Base 3

Best Known (75, 75+45, s)-Nets in Base 3

(75, 75+45, 128)-Net over F₃ — Constructive and digital

Digital (75, 120, 128)-net over F₃, using

4 times m-reduction [i] based on digital (75, 124, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 62, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(75, 75+45, 146)-Net over F₃ — Digital

Digital (75, 120, 146)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+45, 1702)-Net in Base 3 — Upper bound on s

There is no (75, 120, 1703)-net in base 3, because

1 times m-reduction [i] would yield (75, 119, 1703)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 599 606879 279754 530684 853012 510912 455380 025471 627161 058277 > 3¹¹⁹ [i]