MinT - Best Known (6, 69, s)-Nets in Base 25

Best Known (6, 69, s)-Nets in Base 25

(6, 69, 66)-Net over F₂₅ — Constructive and digital

Digital (6, 69, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 69, 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]

(6, 69, 555)-Net in Base 25 — Upper bound on s

There is no (6, 69, 556)-net in base 25, because

19 times m-reduction [i] would yield (6, 50, 556)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 7922 012105 949396 249194 062034 993127 385023 799299 265290 386531 696555 836225 > 25⁵⁰ [i]