Let X be a set of v>=3 elements together with a set B of 3-subset (triples) of X such that every 2-subset of X occurs in exactly one triple of B. Then B is called a Steiner triple system and is a special case of a Steiner system with t = 2 and k = 3. A Steiner triple system S(v) = S(v, k = 3, λ = 1) of order v exists iff v congruent 1, 3 (mod 6). In addition, if Steiner triple systems S_1 and S_2 of orders v_1 and v_2 exist, then so does a Steiner triple system S of order v_1 v_2.

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