MinT - Best Known (40−33, 40, s)-Nets in Base 25

Best Known (40−33, 40, s)-Nets in Base 25

(40−33, 40, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 40, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 40, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(40−33, 40, 715)-Net in Base 25 — Upper bound on s

There is no (7, 40, 716)-net in base 25, because

1 times m-reduction [i] would yield (7, 39, 716)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3 311062 894717 457938 415422 604305 227431 471147 690308 007425 > 25³⁹ [i]