MinT - Best Known (109, 151, s)-Nets in Base 3

Best Known (109, 151, s)-Nets in Base 3

(109, 151, 252)-Net over F₃ — Constructive and digital

Digital (109, 151, 252)-net over F₃, using

3¹ times duplication [i] based on digital (108, 150, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 50, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(109, 151, 453)-Net over F₃ — Digital

Digital (109, 151, 453)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 151, 11679)-Net in Base 3 — Upper bound on s

There is no (109, 151, 11680)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 110624 206082 062026 116242 471396 891198 323995 754454 932696 273629 630896 463681 > 3¹⁵¹ [i]