MinT - Best Known (57−40, 57, s)-Nets in Base 5

Best Known (57−40, 57, s)-Nets in Base 5

(57−40, 57, 42)-Net over F₅ — Constructive and digital

Digital (17, 57, 42)-net over F₅, using

net from sequence [i] based on digital (17, 41)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]

(57−40, 57, 189)-Net in Base 5 — Upper bound on s

There is no (17, 57, 190)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7138 842095 007389 061683 535116 416215 284545 > 5⁵⁷ [i]