MinT - Best Known (40, 109, s)-Nets in Base 25

Best Known (40, 109, s)-Nets in Base 25

(40, 109, 208)-Net over F₂₅ — Constructive and digital

Digital (40, 109, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 109, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(40, 109, 15533)-Net in Base 25 — Upper bound on s

There is no (40, 109, 15534)-net in base 25, because

1 times m-reduction [i] would yield (40, 108, 15534)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 498750 634356 865579 947145 711049 486722 408658 290748 950328 868997 135783 915966 661015 727295 312240 355257 007573 335354 476580 107291 607886 273192 035965 874099 341025 > 25¹⁰⁸ [i]