MinT - Best Known (45−22, 45, s)-Nets in Base 5

Best Known (45−22, 45, s)-Nets in Base 5

(45−22, 45, 52)-Net over F₅ — Constructive and digital

Digital (23, 45, 52)-net over F₅, using

1 times m-reduction [i] based on digital (23, 46, 52)-net over F₅, using
- trace code for nets [i] based on digital (0, 23, 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]

(45−22, 45, 63)-Net over F₅ — Digital

Digital (23, 45, 63)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(45−22, 45, 880)-Net in Base 5 — Upper bound on s

There is no (23, 45, 881)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 704253 898238 660292 674745 972125 > 5⁴⁵ [i]