The [La Jolla Covering repository][1] is a good source for covering designs. Fort and Hedlund determined the minimum size of a $(v,3,2)$-covering design: [Minimal coverings of pairs by triples, Pacific J. Math. 8(4), 709-719, 1958.][2] [1]: https://www.ccrwest.org/cover.html [2]: http://projecteuclid.org/euclid.pjm/1103039697