MinT - Best Known (17, 17+39, s)-Nets in Base 5

Best Known (17, 17+39, s)-Nets in Base 5

(17, 17+39, 42)-Net over F₅ — Constructive and digital

Digital (17, 56, 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+39, 195)-Net in Base 5 — Upper bound on s

There is no (17, 56, 196)-net in base 5, because

1 times m-reduction [i] would yield (17, 55, 196)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 284 382590 706018 427310 515927 527962 124305 > 5⁵⁵ [i]