MinT - Best Known (44−22, 44, s)-Nets in Base 5

Best Known (44−22, 44, s)-Nets in Base 5

(44−22, 44, 52)-Net over F₅ — Constructive and digital

Digital (22, 44, 52)-net over F₅, using

trace code for nets [i] based on digital (0, 22, 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]

(44−22, 44, 58)-Net over F₅ — Digital

Digital (22, 44, 58)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(44−22, 44, 759)-Net in Base 5 — Upper bound on s

There is no (22, 44, 760)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 737771 373342 742038 895432 089825 > 5⁴⁴ [i]