Set systems with three intersections (Q1062054)

Let X be a finite set of cardinality n and \({\mathcal F}^ a \)family of \(4a+5\)-element subsets of X, \(a\geq 6\). Suppose that all the pairwise intersections of members of \({\mathcal F}\) have cardinality 0, a or \(2a+1\). The author proves that \(c_ 1n^{4/3}<\max | {\mathcal F}| <c_ 2n^{4/3}\) for some positive \(c_ 1\), \(c_ 2\).