MinT - Best Known (9, 9+36, s)-Nets in Base 5

Best Known (9, 9+36, s)-Nets in Base 5

(9, 9+36, 26)-Net over F₅ — Constructive and digital

Digital (9, 45, 26)-net over F₅, using

net from sequence [i] based on digital (9, 25)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
  - an explicitly constructive algebraic function field [i]

(9, 9+36, 60)-Net in Base 5 — Upper bound on s

There is no (9, 45, 61)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁵, 61, S₅, 36), but
- the linear programming bound shows that MÂ â‰¥ 5636 577288 736788 204914 773814 380168 914794 921875 / 153 868410 963603 > 5⁴⁵ [i]