MinT - Best Known (86, 86+53, s)-Nets in Base 5

Best Known (86, 86+53, s)-Nets in Base 5

(86, 86+53, 252)-Net over F₅ — Constructive and digital

Digital (86, 139, 252)-net over F₅, using

t-expansion [i] based on digital (85, 139, 252)-net over F₅, using
- 11 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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, 86+53, 358)-Net over F₅ — Digital

Digital (86, 139, 358)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+53, 13506)-Net in Base 5 — Upper bound on s

There is no (86, 139, 13507)-net in base 5, because

1 times m-reduction [i] would yield (86, 138, 13507)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 873007 167147 623982 796835 818820 361832 952407 841208 049427 111104 884742 033592 822589 622195 694946 576665 > 5¹³⁸ [i]