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Keywords:

  • tactical configuration;
  • difference set;
  • inline image-design;
  • partial geometric design

Abstract

In this paper, we introduce a method to construct inline image-designs, which are also known as partial geometric designs, by using subsets of certain finite groups. We introduce the concept of inline image-difference sets and investigate the existence and nonexistence of these structures. We also provide some nonexistence results on inline image-designs based on the fact that inline image-designs yield directed strongly regular graphs.