Transversals in uniform hypergraphs with property (7,2)

Let f(r,p,t) (p>t⩾1, r⩾2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs H possessing the property that every subhypergraph of H with p edges has a transversal of size t. The values of f(r,p,2) for p=3,4,5,6 were found in Erdős et al. (Siberian Adv. Math. 2 (1992) 82–88). We give bounds on f(r,7,2), partially answering a question in Erdős et al. (1992).