MinT - Best Known (108−24, 108, s)-Nets in Base 5

Best Known (108−24, 108, s)-Nets in Base 5

(108−24, 108, 416)-Net over F₅ — Constructive and digital

Digital (84, 108, 416)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (30, 42, 208)-net over F₅, using
  - trace code for nets [i] based on digital (9, 21, 104)-net over F₂₅, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
        a function field by GarcÃa and Quoos [i]
2. digital (42, 66, 208)-net over F₅, using
  - trace code for nets [i] based on digital (9, 33, 104)-net over F₂₅, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₂₅ (see above)

(108−24, 108, 4525)-Net over F₅ — Digital

Digital (84, 108, 4525)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−24, 108, 2582438)-Net in Base 5 — Upper bound on s

There is no (84, 108, 2582439)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3081 491308 104376 478045 401463 163136 116848 600308 656709 146529 873785 562030 181073 > 5¹⁰⁸ [i]