On simplification of certain types of BIBD's (Q1072557)

The authors proves that if \(D\) is the symmetric BIBD \((q^{d+1}-1/q-1,q^d-1/q-1,q^{d-1}-1/q-1)\) constructed from a projective space of dimension \(d\) and order \(q\), then any residual design of the complement of \(D\) is a multiple design consisting of \(q\) copies of a symmetric design with parameters \((q^{d-1}/q-1,q^{d-1},q^{d-1}-q^{d-2})\).