Combinatorics of separation by binary matrices (Q1089343)

Let n be an arbitrary fixed positive integer. Then there exists an integer \(m_ 0\) such that for every \(m\geq m_ 0\) there exists a hypergraph G with m points, the number of lines between \(2m/(n+1)\) and 2m/n, each line containing n points, and such that every set S of points containing at most n points can be uniquely determined from the cardinalities of intersections of S with the lines of G, in a time proportional to m.