MinT - Best Known (52−45, 52, s)-Nets in Base 25

Best Known (52−45, 52, s)-Nets in Base 25

(52−45, 52, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 52, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 52, 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]

(52−45, 52, 645)-Net in Base 25 — Upper bound on s

There is no (7, 52, 646)-net in base 25, because

1 times m-reduction [i] would yield (7, 51, 646)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 202167 867890 170280 969273 916647 723334 264264 043857 151074 935120 590680 270625 > 25⁵¹ [i]