On the construction of \(t\)-designs and the existence of some new infinite families of simple 5-designs
The author continues his work on the construction of infinite families of simple 5-designs. [For his earlier results see Math. Z. 187, 285--287 (1984; Zbl 0537.05007).] Main results of the present paper are further constructions of infinite families of simple 5-designs based on results of the paper loc. cit. and the following theorem; let \((X,B^{(j)})\) be a \(t\)-\((v,k^{(j)},\lambda^{(j)})\) design for \(1\leq j\leq s\) and \(2\leq s\leq t\) such that (1) \(k^{(j)}=k^{(j-1)}+1\), \(2\leq j\leq s\), and \[ (2)\;\sum_{1\leq l\leq s-m}\binom{s-m-1}{s-m-l}\lambda^{(l)}_{t- m}=\lambda^{(1)}_{t-s+1},\;for\;0\leq m\leq s-2. \] Then there exists a \(t\)-\((v+s-1,k^{(s)},\lambda^{(1)}_{t-s+1})\) design, where \(\lambda_ i^{(j)}\) denotes the number of blocks of \((X,B^{(j)})\) containing a given \(i\)-set, \(i\leq t\); \(1\leq j\leq s\).
scientific article; zbMATH DE number 3983167