The Turán Number T(n, k, r)
is the smallest possible number of edges in a k-graph of order
n such that every set of r vertices contains an edge.
exists, but there is no pair (k, r) with
r>k[ges ]3 for which this function could be determined
We give a constructive proof of the upper bound
for every k and r with r[ges ]k[ges ]2.
In the case k=6, r=11 we improve this result, refuting
a conjecture of Turán.