MinT - Best Known (194−54, 194, s)-Nets in Base 3

Best Known (194−54, 194, s)-Nets in Base 3

(194−54, 194, 282)-Net over F₃ — Constructive and digital

Digital (140, 194, 282)-net over F₃, using

1 times m-reduction [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]

(194−54, 194, 555)-Net over F₃ — Digital

Digital (140, 194, 555)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−54, 194, 14614)-Net in Base 3 — Upper bound on s

There is no (140, 194, 14615)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 436182 765823 943570 301248 950985 473350 229449 038413 575554 518795 904228 895274 586594 080525 999531 > 3¹⁹⁴ [i]