MinT - Best Known (86, 110, s)-Nets in Base 5

Best Known (86, 110, s)-Nets in Base 5

(86, 110, 460)-Net over F₅ — Constructive and digital

Digital (86, 110, 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 (44, 68, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 34, 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]

(86, 110, 5203)-Net over F₅ — Digital

Digital (86, 110, 5203)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 110, 3376955)-Net in Base 5 — Upper bound on s

There is no (86, 110, 3376956)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77037 268209 015564 721928 297917 881367 721309 584418 906197 146994 187032 010035 399425 > 5¹¹⁰ [i]