A method for constructing generalized residual designs (Q1068094)

The author gives a construction that utilizes affine planes of order n to produce designs (with possibly repeated blocks) with parameters \(2- ((n+1)^ 2,n+1,n-1)\) that are generalized residual designs in the sense of \textit{S. S. Shrikhande} and \textit{N. M. Singhi} [Utilitas Math. 1, 191- 201 (1972; Zbl 0258.05014)]. He then shows that they can be embedded in a \(2-(n^ 2+3n+3,n+2,n+1)\) design with a block that is repeated b/v times. The generalization is of the residual design with parameters 2-(v-k,k- \(\lambda\),\(\lambda)\) that comes from a (v,k,\(\lambda)\) design; in this case \(b=v\) and there are no repeated blocks.