Private Information Retrieval (PIR) protocols aim at ensuring a user that he can retrieve some part Di of a distributed database D without revealing the index i to the server(s). Most of known PIR protocols focus on decreasing the communication complexity between the client and the server(s). Recently, the use of PIR codes by Fazeli et. al. also lead to a huge reduction of the storage overhead supported by the servers. However, only a few works address the issue of the computational complexity of the servers. In this paper, we show that transversal designs and their generalizations provide PIR schemes achieving simultaneously reasonable communication complexity, low storage overhead, optimal computational complexity for the servers, and resistance to a collusion of some of them.