Constructions for uniform (m, 3)-splitting systems

Suppose m and t are integers such that 0 < t ≤ m. An (m, t)-splitting system is a pair (X,B), where |X| = m and B is a set of subsets of X, called blocks, such that for every Y ⊆ X and |Y | = t, there exists a block B ∈ B such that |B ∩Y | = bt/2c. An (m, t)splitting system is uniform if every block has size bm/2c. We present new construction methods of uniform splitting systems for t = 3 that have a smaller number of blocks as compared to previous results. AMS subject classifications: 05B20, 94A60