Group Divisible Designs With Two Groups and Block Size Five With Fixed Block Configuration

We present constructions and results about GDDs with two groups and block size five in which each block has configuration \((s, t)\), that is, in which each block has exactly \(s\) points from one of the two groups and \(t\) points from the other. After some results for a general \(k\), \(s\), and \(t\), we consider the \((2,3)\) case for block size \(5\). We give new necessary conditions for this family of GDDs and give minimal or near-minimal index examples for all group sizes \(n \geq 4\) except for \(n = 24s + 17\).