On \(4-(10,5,6m)\) Designs with Repeated Blocks

Recently, there has been substantial interest in the problem of the spectrum of possible support sizes of different families of BIB designs. In this paper, we first prove some theorems concerning the spectrum of any \(t\)-design with \(v = 2k\) and \(k = t + 1\), and then we study the spectrum of the case \(4-(10, 5, 6m)\) in more detail.