A method for obtaining small regular bipartite graphs of girth 8

Let q be a prime a power and k an integer such that 3 ≤ k ≤ q . In this paper we present a method using Latin squares to construct adjacency matrices of k -regular bipartite graphs of girth 8 on 2(kq 2 -q) vertices. Some of these graphs have the smallest number of vertices among the known regular graphs with girth 8.