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A u-way (v; k; t) trade is a pair T = (X; T_1; T2,...,T_u) such that for eacht-subset of v-set X the number of blocks containing this t-subset is the samein each Ti (1 <= i <=u). In the other words for each 1 <= i < j <= u, (X; T_i;T_j) is a (v; k; t) trade. There are many questions concerning u-way trades.The main question is about the minimum volume and minimum foundation size ofu-way (v; k; t) trades. In this paper, we determine the minimum volume andminimum foundation size of u-way (v; t + 1; t) trades for each integer number u>2 and t = 2.

The minimum possible volume size of u-way (v, k, t) trades