On the number of minimal transversals in 3-uniform hypergraphs

We prove that the number of minimal transversals (and also the number of maximal independent sets) in a 3-uniform hypergraph with n vertices is at most cn, where c≈1.6702. The best known lower bound for this number, due to Tomescu, is adn, where d=101/5≈1.5849 and a is a constant.