MinT - Best Known (20, 45, s)-Nets in Base 25

Best Known (20, 45, s)-Nets in Base 25

(20, 45, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 45, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 45, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(20, 45, 177)-Net over F₂₅ — Digital

Digital (20, 45, 177)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(20, 45, 29433)-Net in Base 25 — Upper bound on s

There is no (20, 45, 29434)-net in base 25, because

1 times m-reduction [i] would yield (20, 44, 29434)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 32 318526 473635 778572 544383 560636 818981 157330 663006 729929 014465 > 25⁴⁴ [i]