MinT - Best Known (51−29, 51, s)-Nets in Base 5

Best Known (51−29, 51, s)-Nets in Base 5

(51−29, 51, 51)-Net over F₅ — Constructive and digital

Digital (22, 51, 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]

(51−29, 51, 464)-Net in Base 5 — Upper bound on s

There is no (22, 51, 465)-net in base 5, because

1 times m-reduction [i] would yield (22, 50, 465)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 91446 282324 235073 228660 386675 894761 > 5⁵⁰ [i]