MinT - Best Known (53−31, 53, s)-Nets in Base 5

Best Known (53−31, 53, s)-Nets in Base 5

(53−31, 53, 51)-Net over F₅ — Constructive and digital

Digital (22, 53, 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]

(53−31, 53, 414)-Net in Base 5 — Upper bound on s

There is no (22, 53, 415)-net in base 5, because

1 times m-reduction [i] would yield (22, 52, 415)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 239868 578947 708910 921023 930032 541765 > 5⁵² [i]