MinT - Best Known (5, 5+19, s)-Nets in Base 5

Best Known (5, 5+19, s)-Nets in Base 5

(5, 5+19, 20)-Net over F₅ — Constructive and digital

Digital (5, 24, 20)-net over F₅, using

net from sequence [i] based on digital (5, 19)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 5 and N(F) ≥ 20, using
  - an explicitly constructive algebraic function field [i]

(5, 5+19, 57)-Net in Base 5 — Upper bound on s

There is no (5, 24, 58)-net in base 5, because

1 times m-reduction [i] would yield (5, 23, 58)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 13070 737012 891625 > 5²³ [i]