Abstract
The notion of residual and derived design of a symmetric design was introduced in a classic paper by R.C. Bose (1939). A quasi-residual design is a 2-design which has the parameters of a residual design. The embedding problem of quasi-residual design into a symmetric design is an old and natural question. In this survey paper, we discuss various techniques for constructing quasi-residual designs, as well as different types of non-embeddability conditions. We include results for families of non-embeddable quasi-residual designs. Proofs are provided for new results and we give some tables of possible parameter sets of non-embeddable quasi-residual designs.