On an open problem of Paul Turan concerning 3-graphs

The third of Paul Turan’s 1961 list of Research Problems [4] reads: “If 2 ≦ l < k < n, then what is the minimal number μ of combinations C 1,C 2,..., C μ taken l at a time out of 1, 2,..., n with the property that each combination taken k at a time out of 1, 2,..., n contains at least one C j ? (For l = 2 the question is settled with exhibiting the only minimal C-system in my paper “Egy grafelmeleti szelsőertek-feladatrol”, Mat. es Fiz. Lapok (1941) 436–451, in Hungarian with German abstract.)”