MinT - Best Known (52−41, 52, s)-Nets in Base 25

Best Known (52−41, 52, s)-Nets in Base 25

(52−41, 52, 126)-Net over F₂₅ — Constructive and digital

Digital (11, 52, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 52, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(52−41, 52, 1259)-Net in Base 25 — Upper bound on s

There is no (11, 52, 1260)-net in base 25, because

1 times m-reduction [i] would yield (11, 51, 1260)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 197842 891814 520164 785062 568589 747783 512926 761771 434328 496441 989821 002625 > 25⁵¹ [i]