If a Steiner system S(4, 5, 17) exists, it would contain derived S(3, 4, 16) designs. By relying on a recent classification of the S(3, 4, 16), an exhaustive computer search for S(4, 5, 17) is carried out. The search shows that no S(4, 5, 17) exists, thereby ruling out the existence of Steiner systems S(t, t + 1, t + 13) for t 4. Key words: Derived design; Exact cover problem; Steiner system
Patric R. J. Östergård, Olli Pottonen