Date of Award

Spring 2013

Document Type

Thesis

Degree Name

Bachelor of Science

Department

Mathematics

First Advisor

Dr. James Davis

Second Advisor

Dr. Della Dumbaugh

Third Advisor

Dr. Lester Caudill

Abstract

This paper considers the problem of determining which of the 56092 groups of order 256 contain (256; 120; 56; 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 Z4 Z2 . This construction method was able to produce difference sets in 643 of the 649 unsolved groups with the correct normal subgroup. These constructions elimated approximately 90% of the open cases, leaving 81 remaining unsolved groups.

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