MinT - Best Known (50−43, 50, s)-Nets in Base 25

Best Known (50−43, 50, s)-Nets in Base 25

(50−43, 50, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 50, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 50, 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]

(50−43, 50, 650)-Net in Base 25 — Upper bound on s

There is no (7, 50, 651)-net in base 25, because

1 times m-reduction [i] would yield (7, 49, 651)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 324 951202 435008 725357 657250 402976 171259 708097 337173 434363 661607 021225 > 25⁴⁹ [i]