MinT - Best Known (110, 185, s)-Nets in Base 3

Best Known (110, 185, s)-Nets in Base 3

(110, 185, 148)-Net over F₃ — Constructive and digital

Digital (110, 185, 148)-net over F₃, using

1 times m-reduction [i] based on digital (110, 186, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 93, 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]

(110, 185, 168)-Net over F₃ — Digital

Digital (110, 185, 168)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 185, 1692)-Net in Base 3 — Upper bound on s

There is no (110, 185, 1693)-net in base 3, because

1 times m-reduction [i] would yield (110, 184, 1693)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6302 008774 727383 387909 084144 632170 231838 938134 164828 434387 024190 662677 548584 580384 801483 > 3¹⁸⁴ [i]