MinT - Best Known (40, 40+33, s)-Nets in Base 5

Best Known (40, 40+33, s)-Nets in Base 5

(40, 40+33, 104)-Net over F₅ — Constructive and digital

Digital (40, 73, 104)-net over F₅, using

1 times m-reduction [i] based on digital (40, 74, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 37, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(40, 40+33, 116)-Net over F₅ — Digital

Digital (40, 73, 116)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+33, 2364)-Net in Base 5 — Upper bound on s

There is no (40, 73, 2365)-net in base 5, because

1 times m-reduction [i] would yield (40, 72, 2365)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 212 464457 901995 830282 980768 547296 818074 455684 622785 > 5⁷² [i]