MinT - Best Known (165−61, 165, s)-Nets in Base 3

Best Known (165−61, 165, s)-Nets in Base 3

(165−61, 165, 148)-Net over F₃ — Constructive and digital

Digital (104, 165, 148)-net over F₃, using

9 times m-reduction [i] based on digital (104, 174, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 87, 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]

(165−61, 165, 198)-Net over F₃ — Digital

Digital (104, 165, 198)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−61, 165, 2414)-Net in Base 3 — Upper bound on s

There is no (104, 165, 2415)-net in base 3, because

1 times m-reduction [i] would yield (104, 164, 2415)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 787118 419055 030157 782971 889655 202022 466456 523938 990848 154698 892789 417431 327525 > 3¹⁶⁴ [i]