MinT - Best Known (33−16, 33, s)-Nets in Base 5

Best Known (33−16, 33, s)-Nets in Base 5

(33−16, 33, 52)-Net over F₅ — Constructive and digital

Digital (17, 33, 52)-net over F₅, using

1 times m-reduction [i] based on digital (17, 34, 52)-net over F₅, using
- trace code for nets [i] based on digital (0, 17, 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]

(33−16, 33, 54)-Net over F₅ — Digital

Digital (17, 33, 54)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(33−16, 33, 713)-Net in Base 5 — Upper bound on s

There is no (17, 33, 714)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 116715 811041 031216 016257 > 5³³ [i]