MinT - Best Known (17, 17+18, s)-Nets in Base 5

Best Known (17, 17+18, s)-Nets in Base 5

(17, 17+18, 42)-Net over F₅ — Constructive and digital

Digital (17, 35, 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]

(17, 17+18, 46)-Net over F₅ — Digital

Digital (17, 35, 46)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(17, 17+18, 535)-Net in Base 5 — Upper bound on s

There is no (17, 35, 536)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 926712 209615 457127 111265 > 5³⁵ [i]