MinT - Best Known (20, 20+19, s)-Nets in Base 5

Best Known (20, 20+19, s)-Nets in Base 5

(20, 20+19, 52)-Net over F₅ — Constructive and digital

Digital (20, 39, 52)-net over F₅, using

1 times m-reduction [i] based on digital (20, 40, 52)-net over F₅, using
- trace code for nets [i] based on digital (0, 20, 26)-net over F₂₅, using
  - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
      - the rational function field F₂₅(x) [i]
    - Niederreiter sequence [i]

(20, 20+19, 58)-Net over F₅ — Digital

Digital (20, 39, 58)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(20, 20+19, 920)-Net in Base 5 — Upper bound on s

There is no (20, 39, 921)-net in base 5, because

1 times m-reduction [i] would yield (20, 38, 921)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 366 001075 050165 534439 296965 > 5³⁸ [i]