Extending Large Sets oft-Designs

Abstract

A large set of disjointS(λ; t, k, v) designs, denoted byLS(λ; t, k, v), is a partition ofk-subsets of av-set intoS(λ; t, k, v) designs. In this paper, we develop some recursive methods to construct large sets oft-designs. As an application, we construct infinite families of large sets oft-designs for allt. In particular, we show that ifv=2t−3m−2,k=2t−3−1, andt, m⩾2, then a[formula]exists.