Abstract
A 3-way (v,k,t) trade of volume m consists of three disjoint collections T1, T2 and T3, each of m blocks of size k, such that for every t-subset of v-set V, the number of blocks containing this t-subset is the same in each Ti(1≤i≤3). If any t-subset of found(T) occurs at most once in T1(Tj,j≥2), then T is called 3-way (v,k,t) Steiner trade. In this paper the spectrum (that is, the set of allowable volumes) of 3-way (v,k,t) Steiner trades is discussed. Here it is shown that the volume of a 3-way (v,k,2) Steiner trade is at least 3(k−1) for k≠4. Also we show how to construct a 3-way (v,k,2) Steiner trade of volume m when m≥12(k−1) for k≥15, or m is multiple of three and 3(k−1)≤m≤12(k−1).
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