MinT - Best Known (55−33, 55, s)-Nets in Base 5

Best Known (55−33, 55, s)-Nets in Base 5

(55−33, 55, 51)-Net over F₅ — Constructive and digital

Digital (22, 55, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(55−33, 55, 377)-Net in Base 5 — Upper bound on s

There is no (22, 55, 378)-net in base 5, because

1 times m-reduction [i] would yield (22, 54, 378)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 57 317138 466827 871772 803594 634772 423425 > 5⁵⁴ [i]