MinT - Best Known (87, 87+36, s)-Nets in Base 9

Best Known (87, 87+36, s)-Nets in Base 9

(87, 87+36, 756)-Net over F₉ — Constructive and digital

Digital (87, 123, 756)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 19, 16)-net over F₉, using
  - net from sequence [i] based on digital (1, 15)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
      - a function field by GarcÃa and Quoos [i]
2. digital (68, 104, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 52, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(87, 87+36, 3941)-Net over F₉ — Digital

Digital (87, 123, 3941)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+36, 3131091)-Net in Base 9 — Upper bound on s

There is no (87, 123, 3131092)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2354 130308 580992 723184 480396 311170 812344 088240 862831 320009 801170 463168 720072 740658 328499 691191 064443 492589 855904 518081 > 9¹²³ [i]