Quasi-residual designs, 112-designs, and strongly regular multigraphs Original Research Article

It is shown that a quasi-residual 2-(v, k, λ) design is the residuum of a symmetric design provided that k > cλ4 for a constant number c. This result improves earlier results of Bose et al. (1976) and Neumaier (1982), who proved the result for k >12λ5 + 0(λ4). This embedding theorem will be a consequence of more general characterization theorems for certain strongly regular multigraphs (see Theorem 2 and its corollary in the introduction).