Applying balanced generalized weighing matrices to construct block designs (Q5925763)

The paper gives a recursive construction of symmetric 2-\((v,k,\lambda)\) designs with NEWLINE\[NEWLINEv= 1+qr(r^{m+ 1}- 1)/(r- 1),\qquad k= r^m,\qquad \lambda= (r- 1)r^{m-1}/q,NEWLINE\]NEWLINE where \(m\) is any positive integer, and \(q\) and \(r= (q^d- 1)/(q- 1)\) are prime powers. A similar construction yields an infinite family of non-embeddable quasi-residual designs. The non-embeddability is proved by showing that certain triples of blocks cannot be extended to blocks of a symmetric design. Both constructions use balanced generalized weighing matrices with classical parameters.