Abstract:Let m and t be positive integers with t 2. An (m, t)-splitting system is a pair (X, B) where |X| = m and B is a collection of subsets of X called blocks such that for every Y ⊆ X with |Y | = t, there exists a block B ∈ B such that |B ∩ Y | = t/2 . An (m, t)-splitting system is uniform if every block has size m/2 . In this paper, we give several constructions and bounds for splitting systems, concentrating mainly on the case t = 3. We consider uniform splitting systems as well as other splitting systems with sp… Show more
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