MinT - Best Known (101−75, 101, s)-Nets in Base 25

Best Known (101−75, 101, s)-Nets in Base 25

(101−75, 101, 200)-Net over F₂₅ — Constructive and digital

Digital (26, 101, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 101, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(101−75, 101, 3644)-Net in Base 25 — Upper bound on s

There is no (26, 101, 3645)-net in base 25, because

1 times m-reduction [i] would yield (26, 100, 3645)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 62 763039 005252 413383 808526 713671 429405 845105 866992 733072 507806 842090 579077 817548 856090 802761 650960 612963 065248 704352 724460 146173 075836 266265 > 25¹⁰⁰ [i]