MinT - Best Known (89−82, 89, s)-Nets in Base 25

Best Known (89−82, 89, s)-Nets in Base 25

(89−82, 89, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 89, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 89, 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]

(89−82, 89, 639)-Net in Base 25 — Upper bound on s

There is no (7, 89, 640)-net in base 25, because

32 times m-reduction [i] would yield (7, 57, 640)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 48 659566 175148 101512 620834 056263 397453 835362 908184 627649 101778 555400 862409 268225 > 25⁵⁷ [i]