The support sizes of MPT(v, 3)
Abstract
The support size SS(v, 3) of a maximum packing of triples of order v and index 3, MPT(v, 3), is the number of distinct triples appearing in it. We establish strong necessary conditions on the spectrum of support sizes for a MPT(v, 3) and, for some subset of SS(v, 3), we find a sufficient condition.