MinT - Best Known (42, 42+57, s)-Nets in Base 25

Best Known (42, 42+57, s)-Nets in Base 25

(42, 42+57, 288)-Net over F₂₅ — Constructive and digital

Digital (42, 99, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 99, 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]

(42, 42+57, 36762)-Net in Base 25 — Upper bound on s

There is no (42, 99, 36763)-net in base 25, because

1 times m-reduction [i] would yield (42, 98, 36763)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 99570 417540 698428 313952 623355 432662 827751 760969 582193 227816 541758 019540 634537 609635 087221 028017 364016 207875 931234 765254 804997 129893 677025 > 25⁹⁸ [i]