The Spectrum of Support Sizes of \(BIB\) Designs with \(v= 10\) and \(k=5\)

The support of a \(t\)-design is the set of all distinct blocks of the design. The support size of a design is denoted by \(b^*\). In this paper, except for \(b^* = 23\), we completely determine the spectrum of support sizes of the case \(v = 10\), \(k = 5\), and \(t = 2\).