MinT - Best Known (22−11, 22, s)-Nets in Base 5

Best Known (22−11, 22, s)-Nets in Base 5

(22−11, 22, 52)-Net over F₅ — Constructive and digital

Digital (11, 22, 52)-net over F₅, using

trace code for nets [i] based on digital (0, 11, 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]

(22−11, 22, 558)-Net in Base 5 — Upper bound on s

There is no (11, 22, 559)-net in base 5, because

1 times m-reduction [i] would yield (11, 21, 559)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 479 443850 843309 > 5²¹ [i]