MinT - Best Known (47, 110, s)-Nets in Base 25

Best Known (47, 110, s)-Nets in Base 25

(47, 110, 288)-Net over F₂₅ — Constructive and digital

Digital (47, 110, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 110, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

(47, 110, 42559)-Net in Base 25 — Upper bound on s

There is no (47, 110, 42560)-net in base 25, because

1 times m-reduction [i] would yield (47, 109, 42560)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 237 535803 481504 883188 860648 345293 106671 795793 003366 364053 553169 466280 570775 635841 979925 764945 286978 349863 991997 239049 846890 462274 219261 886758 952699 900417 > 25¹⁰⁹ [i]