MinT - Best Known (141, 141+55, s)-Nets in Base 3

Best Known (141, 141+55, s)-Nets in Base 3

(141, 141+55, 282)-Net over F₃ — Constructive and digital

Digital (141, 196, 282)-net over F₃, using

3¹ times duplication [i] based on digital (140, 195, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 65, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(141, 141+55, 544)-Net over F₃ — Digital

Digital (141, 196, 544)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+55, 15222)-Net in Base 3 — Upper bound on s

There is no (141, 196, 15223)-net in base 3, because

1 times m-reduction [i] would yield (141, 195, 15223)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1093 235229 816555 461775 660427 261767 759885 637868 791904 491175 375216 098907 338016 731758 801677 725483 > 3¹⁹⁵ [i]