MinT - Best Known (109−65, 109, s)-Nets in Base 25

Best Known (109−65, 109, s)-Nets in Base 25

(109−65, 109, 288)-Net over F₂₅ — Constructive and digital

Digital (44, 109, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 109, 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]

(109−65, 109, 27826)-Net in Base 25 — Upper bound on s

There is no (44, 109, 27827)-net in base 25, because

1 times m-reduction [i] would yield (44, 108, 27827)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 504201 914641 644509 703812 146543 679546 221077 160557 899899 220872 975490 199313 674605 791617 867818 707783 974407 686708 129664 068935 329147 868366 742606 484011 655425 > 25¹⁰⁸ [i]