MinT - Best Known (28, 28+17, s)-Nets in Base 5

Best Known (28, 28+17, s)-Nets in Base 5

(28, 28+17, 132)-Net over F₅ — Constructive and digital

Digital (28, 45, 132)-net over F₅, using

3 times m-reduction [i] based on digital (28, 48, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 24, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(28, 28+17, 165)-Net over F₅ — Digital

Digital (28, 45, 165)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 28+17, 6570)-Net in Base 5 — Upper bound on s

There is no (28, 45, 6571)-net in base 5, because

1 times m-reduction [i] would yield (28, 44, 6571)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 687443 421566 077785 486940 382945 > 5⁴⁴ [i]