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A µ-way (v, k, t) trade T = {T 1 , T 2 , ..., T µ } of volume m consists of µ disjoint collections T 1 , T 2 , ..., T µ , 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 T i (forIn this paper we characterize the 3-way 3-homogeneous (v, 3, 2) Steiner trades of volume v. Also we show how to construct a 3-way d-homogeneous (v, 3, 2) Steiner trade for d ∈ {4, 5, 6}, except for seven small values of v.

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