On the existence of an infinite family of simple 5-designs
\textit{W. O. Alltop} [J. Comb. Theory, Ser. A 12, 390--395 (1972; Zbl 0239.05011)] constructed for the first time an infinite class of simple \(5-(2^ n+2,2^{n-1}+1,(2^{n-1}-3)(2^{n-2}-1))\) designs for \(n\geq 4\). That was the only infinite class of simple 5-designs known until now. We give a construction of a \(t\)-design from another design. In particular, using the 5-designs of Alltop, we can prove the existence of a new infinite family of simple \(5-(2^ n+3,2^{n-1}+1,(2^ n-2)(2^{n-1}- 3)(2^{n-2}-1))\) designs for \(n\geq 5\). Further infinite families of 4-designs have been found by using this construction on the known series of 4-designs.
scientific article; zbMATH DE number 3853085