MinT - Best Known (109−39, 109, s)-Nets in Base 5

Best Known (109−39, 109, s)-Nets in Base 5

(109−39, 109, 252)-Net over F₅ — Constructive and digital

Digital (70, 109, 252)-net over F₅, using

11 times m-reduction [i] based on digital (70, 120, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 60, 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]

(109−39, 109, 380)-Net over F₅ — Digital

Digital (70, 109, 380)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−39, 109, 18617)-Net in Base 5 — Upper bound on s

There is no (70, 109, 18618)-net in base 5, because

1 times m-reduction [i] would yield (70, 108, 18618)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3082 214818 147999 770539 392790 585887 523109 271011 831838 912977 983664 923714 470025 > 5¹⁰⁸ [i]