Difference Sets and the Symmetric Difference Property

With the intent to discover block designs from groups of order 256 and higher that have the symmetric difference property, we analyze these block designs through products of groups that give smaller block designs with the symmetric difference property (SDP). This research expands upon the knowledge of SDP designs by looking at designs that come from groups of extremely high orders, which we analyze by looking at the difference sets of these groups. This will give way to new SDP designs that can be analyzed and studied in the near future.