MinT - Best Known (18−13, 18, s)-Nets in Base 25

Best Known (18−13, 18, s)-Nets in Base 25

(18−13, 18, 66)-Net over F₂₅ — Constructive and digital

Digital (5, 18, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 18, 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]

(18−13, 18, 1137)-Net in Base 25 — Upper bound on s

There is no (5, 18, 1138)-net in base 25, because

1 times m-reduction [i] would yield (5, 17, 1138)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 584889 192081 804609 322849 > 25¹⁷ [i]