MinT - Best Known (87, 87+24, s)-Nets in Base 5

Best Known (87, 87+24, s)-Nets in Base 5

(87, 87+24, 460)-Net over F₅ — Constructive and digital

Digital (87, 111, 460)-net over F₅, using

1 times m-reduction [i] based on digital (87, 112, 460)-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 (45, 70, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 35, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
        the Hermitian function field over F₂₅ [i]

(87, 87+24, 5579)-Net over F₅ — Digital

Digital (87, 111, 5579)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+24, 3861650)-Net in Base 5 — Upper bound on s

There is no (87, 111, 3861651)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 385186 148166 792212 809475 209714 002542 317084 294240 861966 469254 983713 781590 777425 > 5¹¹¹ [i]