Symmetric \((49, 16,5)\) Designs

In this paper the existence of the \(12140\) non-isomorphic symmetric \((49,16,5)\) designs with an involutory homology (this is a special kind of involution acting on a design) is propagated. The automorphism groups are cyclic of orders \(2\), \(4\), \(8\), or \(10\). \(218\) designs are self-dual. The \(40\) designs with an automorphism group of order \(10\) were already given in [2]. A computer (IBM \(3090\)) was used for about \(36\) hours CPU time. According to [2,4] now there are known \(12146\) symmetric \((49,16,5)\) designs.