MinT - Best Known (45−39, 45, s)-Nets in Base 25

Best Known (45−39, 45, s)-Nets in Base 25

(45−39, 45, 66)-Net over F₂₅ — Constructive and digital

Digital (6, 45, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 45, 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]

(45−39, 45, 560)-Net in Base 25 — Upper bound on s

There is no (6, 45, 561)-net in base 25, because

1 times m-reduction [i] would yield (6, 44, 561)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 32 465932 536031 973522 169670 857953 776515 222246 903374 332658 185225 > 25⁴⁴ [i]