On symmetric block designs (40, 13, 4) with automorphisms of order 5

A classification of all symmetric block designs of order nine with an automorphism of order six

“…As a matter of fact, the classification for the parameters (35,17,8), (56,11,2), and (91,10,1) had already been done, and in this paper we present the results for the parameters (36,15,6), (40,13,4), and (45,12,3). We also provide information about the order and the structure of the full automorphism groups of the constructed designs.…”

Ovoids of generalized quadrangles of order and Delsarte cocliques in related strongly regular graphs

“…Except for q ∈ {2, 3}, the existence of a generalized quadrangle of order (q, q 2 − q) is open, so our results may only apply to an empty set. See [14,Chapter 6] for the unique existing generalized quadrangle of order (2, 2) and the non-existence of generalized quadrangles of order (3,6). As shown in [3, Section 1.15], the parameters of the point graph of a generalized quadrangle of order (q, q 2 − q) are as follows, where q is an integer larger than 1.…”

“…By Theorem 1.2, we obtain a symmetric 2-(40, 13, 4) design. Many such designs are known [6,15] (for example, we can take the 1-dimensional subspaces of F Proof. Recall that an ovoid has size m − .…”

Enumeration of Strongly Regular Graphs on up to 50 Vertices Having S3 as an Automorphism Group

“…The vector: p n r = (x 0 , x n r ; y (11), (13), (14) and (15) is called a prototype for a row corresponding to the orbit of length n r . Using prototypes, we construct an orbit matrix row by row.…”

“…Our last step is the construction of the corresponding orbit matrices for the subgroup H 0 = {1}, i.e., construction of adjacency matrices of the strongly regular graphs. The concept of the G-isomorphism of two-block designs was introduced in [14]. For the elimination of mutually-isomorphic structures, we use the concept of G-isomorphism.…”