MinT - Best Known (192−77, 192, s)-Nets in Base 3

Best Known (192−77, 192, s)-Nets in Base 3

(192−77, 192, 148)-Net over F₃ — Constructive and digital

Digital (115, 192, 148)-net over F₃, using

4 times m-reduction [i] based on digital (115, 196, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 98, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(192−77, 192, 179)-Net over F₃ — Digital

Digital (115, 192, 179)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−77, 192, 1841)-Net in Base 3 — Upper bound on s

There is no (115, 192, 1842)-net in base 3, because

1 times m-reduction [i] would yield (115, 191, 1842)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 536737 304924 018219 574275 769213 718270 588072 940968 197747 208361 285923 832631 064508 258817 899933 > 3¹⁹¹ [i]