MinT - Best Known (110, 110+67, s)-Nets in Base 3

Best Known (110, 110+67, s)-Nets in Base 3

(110, 110+67, 148)-Net over F₃ — Constructive and digital

Digital (110, 177, 148)-net over F₃, using

9 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, 110+67, 197)-Net over F₃ — Digital

Digital (110, 177, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+67, 2274)-Net in Base 3 — Upper bound on s

There is no (110, 177, 2275)-net in base 3, because

1 times m-reduction [i] would yield (110, 176, 2275)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 950171 408598 131507 332096 548329 893966 097942 061279 238975 403009 844278 935863 348019 174023 > 3¹⁷⁶ [i]