Group divisible designs with block size four and group type \(g^um^1\)
In this paper the authors consider the existence problem for \(\{4\}\)-GDDs of type \(g^{u}m^{1}\) and show that the necessary conditions for the existence of such a GDD with \(g,m>0\) and \(u\geq 4\), are also sufficient except for \((g,m,u)=(2,6,5)\) and except possibly for some cases listed in the paper. Some possible exceptions can be removed from the list by constructing \(\{4\}\)-GDDs of type \(2^{39}35^{1}\), \(6^{13}27^{1}\) and \(6^{13}33^{1}\) or of type \(g^{6}m^{1}\) with \(g\equiv 2,4 \pmod 6\).
scientific article; zbMATH DE number 6390340