MinT - Best Known (7, 7+47, s)-Nets in Base 25

Best Known (7, 7+47, s)-Nets in Base 25

(7, 7+47, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 54, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 54, 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]

(7, 7+47, 642)-Net in Base 25 — Upper bound on s

There is no (7, 54, 643)-net in base 25, because

1 times m-reduction [i] would yield (7, 53, 643)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 127 207712 018162 431040 052311 963550 933322 681622 188707 623848 922602 566691 845625 > 25⁵³ [i]