Abstract
A (v,3,2)-covering is a family of 3-subsets of a v-set, called blocks, such that any two elements of v-set appear in at least one of the blocks. In this paper, we propose new construction of (v,3,2)-coverings with the minimum number of blocks. This construction represents a generalization of Bose?s and Skolem?s constructions of Steiner systems S(2,3,6n+3) and S(2,3,6n+1). Unlike the existing constructions, our construction is direct and it uses the set of base blocks and permutation p, so by applying it the remaining blocks of (v,3,2)-covering are obtained.
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