MinT - Best Known (106−56, 106, s)-Nets in Base 9

Best Known (106−56, 106, s)-Nets in Base 9

(106−56, 106, 106)-Net over F₉ — Constructive and digital

Digital (50, 106, 106)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 33, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 73, 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]

(106−56, 106, 182)-Net over F₉ — Digital

Digital (50, 106, 182)-net over F₉, using

net from sequence [i] based on digital (50, 181)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
  - a curve from the manYPoints database [i]

(106−56, 106, 5769)-Net in Base 9 — Upper bound on s

There is no (50, 106, 5770)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141594 116421 468428 601052 681946 934483 720900 330441 948211 432901 716050 422183 965204 987306 881226 800937 752129 > 9¹⁰⁶ [i]