MinT - Best Known (109, 109+43, s)-Nets in Base 3

Best Known (109, 109+43, s)-Nets in Base 3

(109, 109+43, 246)-Net over F₃ — Constructive and digital

Digital (109, 152, 246)-net over F₃, using

1 times m-reduction [i] based on digital (109, 153, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 51, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(109, 109+43, 429)-Net over F₃ — Digital

Digital (109, 152, 429)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+43, 11679)-Net in Base 3 — Upper bound on s

There is no (109, 152, 11680)-net in base 3, because

1 times m-reduction [i] would yield (109, 151, 11680)-net in base 3, but
- 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]