MinT - Best Known (112−56, 112, s)-Nets in Base 9

Best Known (112−56, 112, s)-Nets in Base 9

(112−56, 112, 164)-Net over F₉ — Constructive and digital

Digital (56, 112, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 56, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(112−56, 112, 217)-Net over F₉ — Digital

Digital (56, 112, 217)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−56, 112, 9248)-Net in Base 9 — Upper bound on s

There is no (56, 112, 9249)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75050 045046 029823 880740 762120 789342 881669 802833 898977 882221 286713 444852 915446 179704 208943 809921 913002 720097 > 9¹¹² [i]