MinT - Best Known (119−33, 119, s)-Nets in Base 3

Best Known (119−33, 119, s)-Nets in Base 3

(119−33, 119, 228)-Net over F₃ — Constructive and digital

Digital (86, 119, 228)-net over F₃, using

1 times m-reduction [i] based on digital (86, 120, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 40, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(119−33, 119, 381)-Net over F₃ — Digital

Digital (86, 119, 381)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−33, 119, 11211)-Net in Base 3 — Upper bound on s

There is no (86, 119, 11212)-net in base 3, because

1 times m-reduction [i] would yield (86, 118, 11212)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199 702643 568781 327379 720402 797458 054571 722219 306729 586305 > 3¹¹⁸ [i]