Super-simple BIBDs with block size 4 and index 7
A design is called simple if it contains no repeated blocks. A design is said to be super-simple if the intersection of any two blocks has at most two elements. The main result of this paper, deduced by direct and recursive constructions is the following: The necessary conditions for existence of a super-simple \((v,4,7)\)-BIBD, namely \(v\equiv 1, 4\) (mod 12) and \(v\geq 16\), are also sufficient. Note that the existence of super-simple \((v,4,\lambda)\)-BIBDs has been previously determined for \(\lambda=2,3,4,5,6\) and \(9\) and when \(\lambda =7\), only the necessary conditions were known.
scientific article; zbMATH DE number 7257923
scientific article