Constructions for uniform (m, 3)-splitting systems

Abstract

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 subset of X and \Y\ = t, there exists a block B is an element of B such that \B boolean AND Y\ = left perpendiculart/2rightperpendicular. An (m, t)-splitting system is uniform if every block has size left perpendicularm/2right perpendicular. We present new construction methods of uniform splitting systems for t = 3 that have a smaller number of blocks as compared to previous results.