Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...

Van Lint and Tonchev (1993, J. Combin. Theory Ser. A 62, 252 260) described a sufficient condition for the non-embeddability of a quasi-derived design into a symmetric balanced incomplete block design. In this paper, by using the notion of incomplete designs, this criterion is changed to find certain quasi-derived designs in some special cases. Many infinite series of non-embeddable quasi-deriv...