MinT - Best Known (67−45, 67, s)-Nets in Base 5

Best Known (67−45, 67, s)-Nets in Base 5

(67−45, 67, 51)-Net over F₅ — Constructive and digital

Digital (22, 67, 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]

(67−45, 67, 267)-Net in Base 5 — Upper bound on s

There is no (22, 67, 268)-net in base 5, because

1 times m-reduction [i] would yield (22, 66, 268)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14351 277895 457346 049229 183364 599507 655044 117825 > 5⁶⁶ [i]