MinT - Best Known (44−37, 44, s)-Nets in Base 25

Best Known (44−37, 44, s)-Nets in Base 25

(44−37, 44, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 44, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 44, 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]

(44−37, 44, 678)-Net in Base 25 — Upper bound on s

There is no (7, 44, 679)-net in base 25, because

1 times m-reduction [i] would yield (7, 43, 679)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 307863 698490 653139 780118 152813 330005 306726 006250 007130 868945 > 25⁴³ [i]