MinT - Best Known (189−54, 189, s)-Nets in Base 3

Best Known (189−54, 189, s)-Nets in Base 3

(189−54, 189, 264)-Net over F₃ — Constructive and digital

Digital (135, 189, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 63, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(189−54, 189, 496)-Net over F₃ — Digital

Digital (135, 189, 496)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−54, 189, 11919)-Net in Base 3 — Upper bound on s

There is no (135, 189, 11920)-net in base 3, because

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]