Linked systems of symmetric group divisible designs
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We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which are linked. Several examples of linked systems of symmetric group divisible designs are provided.
KeywordsSymmetric group divisible design Association scheme Mutually orthogonal Latin square Mutually UFS Latin square Generalized Hadamard matrix
The authors are grateful to anonymous referees for many suggestions and corrections which have improved the presentation of the paper very much. Hadi Kharaghani is supported by an NSERC Discovery Grant. Sho Suda is supported by JSPS KAKENHI Grant Number 15K21075.
- 6.Holzmann, W.H., Kharaghani, H., Suda, S.: Mutually unbiased biangular vectors and association schemes. In: Colbourn, C.J. (eds.) Algebraic Design Theory and Hadamard Matrices, Volume 133 of Springer Proceedings in Mathematics Statistics, pp. 149–157. Springer International Publishing (2015)Google Scholar