MinT - Best Known (103−40, 103, s)-Nets in Base 5

Best Known (103−40, 103, s)-Nets in Base 5

(103−40, 103, 252)-Net over F₅ — Constructive and digital

Digital (63, 103, 252)-net over F₅, using

3 times m-reduction [i] based on digital (63, 106, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 53, 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]

(103−40, 103, 261)-Net over F₅ — Digital

Digital (63, 103, 261)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−40, 103, 8244)-Net in Base 5 — Upper bound on s

There is no (63, 103, 8245)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 986599 046933 903909 243009 989614 138886 780830 086049 422317 691947 005715 747505 > 5¹⁰³ [i]