MinT - Best Known (13−9, 13, s)-Nets in Base 5

Best Known (13−9, 13, s)-Nets in Base 5

(13−9, 13, 18)-Net over F₅ — Constructive and digital

Digital (4, 13, 18)-net over F₅, using

net from sequence [i] based on digital (4, 17)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 4 and N(F) ≥ 18, using
  - an explicitly constructive algebraic function field [i]

(13−9, 13, 66)-Net in Base 5 — Upper bound on s

There is no (4, 13, 67)-net in base 5, because

1 times m-reduction [i] would yield (4, 12, 67)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 248 357745 > 5¹² [i]