MinT - Best Known (26−17, 26, s)-Nets in Base 5

Best Known (26−17, 26, s)-Nets in Base 5

(26−17, 26, 26)-Net over F₅ — Constructive and digital

Digital (9, 26, 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]

(26−17, 26, 138)-Net in Base 5 — Upper bound on s

There is no (9, 26, 139)-net in base 5, because

1 times m-reduction [i] would yield (9, 25, 139)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 307636 138024 750817 > 5²⁵ [i]