MinT - Best Known (88, 88+36, s)-Nets in Base 9

Best Known (88, 88+36, s)-Nets in Base 9

(88, 88+36, 760)-Net over F₉ — Constructive and digital

Digital (88, 124, 760)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 20, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, 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]

(88, 88+36, 4195)-Net over F₉ — Digital

Digital (88, 124, 4195)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+36, 3537605)-Net in Base 9 — Upper bound on s

There is no (88, 124, 3537606)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21187 163276 441421 572539 388148 254611 657505 016128 414697 633613 805854 661206 293798 984037 779828 333892 973069 968113 038560 815777 > 9¹²⁴ [i]