MinT - Best Known (193−79, 193, s)-Nets in Base 3

Best Known (193−79, 193, s)-Nets in Base 3

(193−79, 193, 148)-Net over F₃ — Constructive and digital

Digital (114, 193, 148)-net over F₃, using

1 times m-reduction [i] based on digital (114, 194, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 97, 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]

(193−79, 193, 170)-Net over F₃ — Digital

Digital (114, 193, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−79, 193, 1680)-Net in Base 3 — Upper bound on s

There is no (114, 193, 1681)-net in base 3, because

1 times m-reduction [i] would yield (114, 192, 1681)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 529098 445892 309531 366287 703096 711448 427772 562030 872940 691668 462498 325756 095719 551339 791947 > 3¹⁹² [i]