MinT - Best Known (191−53, 191, s)-Nets in Base 3

Best Known (191−53, 191, s)-Nets in Base 3

(191−53, 191, 282)-Net over F₃ — Constructive and digital

Digital (138, 191, 282)-net over F₃, using

1 times m-reduction [i] based on digital (138, 192, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 64, 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]

(191−53, 191, 554)-Net over F₃ — Digital

Digital (138, 191, 554)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−53, 191, 16152)-Net in Base 3 — Upper bound on s

There is no (138, 191, 16153)-net in base 3, because

1 times m-reduction [i] would yield (138, 190, 16153)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 503433 215179 642639 301296 992718 570461 758425 252985 828726 850430 487450 376542 628666 858974 495705 > 3¹⁹⁰ [i]