MinT - Best Known (135, 135+55, s)-Nets in Base 3

Best Known (135, 135+55, s)-Nets in Base 3

(135, 135+55, 252)-Net over F₃ — Constructive and digital

Digital (135, 190, 252)-net over F₃, using

3¹ times duplication [i] based on digital (134, 189, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 63, 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]

(135, 135+55, 477)-Net over F₃ — Digital

Digital (135, 190, 477)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+55, 11919)-Net in Base 3 — Upper bound on s

There is no (135, 190, 11920)-net in base 3, because

1 times m-reduction [i] would yield (135, 189, 11920)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 500726 534866 576671 028921 276347 080194 170779 601938 802289 790361 895725 895443 054373 839794 012225 > 3¹⁸⁹ [i]