There exists no Steiner system S(4, 5, 17)

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

• Type: Journal
• Year: 2008
• Where: JCT
• Authors: Patric R. J. Östergård, Olli Pottonen
• Keywords: Design, Exact Cover Problem, JCT 2008, Steiner System