The Higman-Sims design is an incidence structure of 176 points and 176 blocks of cardinality 50 with every two blocks meeting in 14 points. The automorphism group of this design is the Higman-Sims simple group. We demonstrate that the point set and the block set of the Higman-Sims design can be partitioned into subsets X1, X2,...,X11 and B1, B2,...,B11, respectively, so that the substructures (Xi, Bi), i = 1, 2,...,11, are isomorphic symmetric (16, 6, 2)-designs.
Yury J. Ionin, Professor, Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859 firstname.lastname@example.org
Klee, Steven and Yates, Leah
"Tight Subdesigns of the Higman-Sims Design,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 5
, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol5/iss2/9