MinT - Best Known (192−85, 192, s)-Nets in Base 3

Best Known (192−85, 192, s)-Nets in Base 3

(192−85, 192, 80)-Net over F₃ — Constructive and digital

Digital (107, 192, 80)-net over F₃, using

6 times m-reduction [i] based on digital (107, 198, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 99, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(192−85, 192, 136)-Net over F₃ — Digital

Digital (107, 192, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−85, 192, 1179)-Net in Base 3 — Upper bound on s

There is no (107, 192, 1180)-net in base 3, because

1 times m-reduction [i] would yield (107, 191, 1180)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 692282 483847 343393 445743 533757 627629 506708 403972 519583 716103 548199 657403 622379 929477 064649 > 3¹⁹¹ [i]