MinT - Best Known (22, 59, s)-Nets in Base 5

Best Known (22, 59, s)-Nets in Base 5

(22, 59, 51)-Net over F₅ — Constructive and digital

Digital (22, 59, 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]

(22, 59, 324)-Net in Base 5 — Upper bound on s

There is no (22, 59, 325)-net in base 5, because

1 times m-reduction [i] would yield (22, 58, 325)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 35246 709603 348924 906015 233568 308947 436761 > 5⁵⁸ [i]