There exists no Steiner system

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 .