A direct method to construct triple systems

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Abstract

A triple system is a balanced incomplete block design D(v, k, λ, b, r) with k = 3. Although it has been shown that triple systems exist for all values of the parameters satisfying the necessary conditions: λ(ν − 1) ≡ 0 (mod 2), λν(ν − 1) ≡ 0 (mod 6), direct methods (nonrecursive) of construction are not available in general. In this paper we give a direct method to construct a triple system for all values of the parameters satisfying the necessary conditions.

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