Dukes, Peter J.Ling, Alan C. H.2019-01-242019-01-2420172017Dukes, P. J. & Ling, A. C. H. (2017). Relative difference sets partitioned by cosets. The Electronic Journal of Combinatorics, 24(3), article P3.64.https://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p64http://hdl.handle.net/1828/10538We explore classical (relative) difference sets intersected with the cosets of a subgroup of small index. The intersection sizes are governed by quadratic Diophantine equations. Developing the intersections in the subgroup yields an interesting class of group divisible designs. From this and the Bose-Shrikhande-Parker construction, we obtain some new sets of mutually orthogonal latin squares. We also briefly consider optical orthogonal codes and difference triangle systems.enrelative difference setmutually orthogonal latin squareoptical orthogonal codedifference triangle systemArticleDepartment of Mathematics and Statistics