MinT - Best Known (12, 12+11, s)-Nets in Base 5

Best Known (12, 12+11, s)-Nets in Base 5

(12, 12+11, 52)-Net over F₅ — Constructive and digital

Digital (12, 23, 52)-net over F₅, using

1 times m-reduction [i] based on digital (12, 24, 52)-net over F₅, using
- trace code for nets [i] based on digital (0, 12, 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]

(12, 12+11, 771)-Net in Base 5 — Upper bound on s

There is no (12, 23, 772)-net in base 5, because

1 times m-reduction [i] would yield (12, 22, 772)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2389 531186 803601 > 5²² [i]