MinT - Best Known (91, 91+26, s)-Nets in Base 5

Best Known (91, 91+26, s)-Nets in Base 5

(91, 91+26, 460)-Net over F₅ — Constructive and digital

Digital (91, 117, 460)-net over F₅, using

1 times m-reduction [i] based on digital (91, 118, 460)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (31, 44, 208)-net over F₅, using
    - trace code for nets [i] based on digital (9, 22, 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 (47, 74, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 37, 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]

(91, 91+26, 4763)-Net over F₅ — Digital

Digital (91, 117, 4763)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+26, 2767418)-Net in Base 5 — Upper bound on s

There is no (91, 117, 2767419)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6018 557025 344068 241716 105872 017927 603198 995055 370368 284835 207614 529677 065555 663037 > 5¹¹⁷ [i]