MinT - Best Known (19−13, 19, s)-Nets in Base 5

Best Known (19−13, 19, s)-Nets in Base 5

(19−13, 19, 21)-Net over F₅ — Constructive and digital

Digital (6, 19, 21)-net over F₅, using

net from sequence [i] based on digital (6, 20)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 6 and N(F) ≥ 21, using
  - an explicitly constructive algebraic function field [i]

(19−13, 19, 89)-Net in Base 5 — Upper bound on s

There is no (6, 19, 90)-net in base 5, because

1 times m-reduction [i] would yield (6, 18, 90)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 908489 411713 > 5¹⁸ [i]