MinT - Best Known (165, 235, s)-Nets in Base 3

Best Known (165, 235, s)-Nets in Base 3

(165, 235, 252)-Net over F₃ — Constructive and digital

Digital (165, 235, 252)-net over F₃, using

3¹ times duplication [i] based on digital (164, 234, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 78, 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]

(165, 235, 522)-Net over F₃ — Digital

Digital (165, 235, 522)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 235, 11076)-Net in Base 3 — Upper bound on s

There is no (165, 235, 11077)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13298 426602 664442 752598 168224 261721 945568 780904 802927 906025 571225 309989 957176 214425 330569 537664 975500 935612 620651 > 3²³⁵ [i]