On the covering of pairs by quadruples (Q1080428)

The author shows that the Schoenheim bound is always precise for covering designs with block size 4 and all \(\lambda >1\). The work is a natural extension of Mills' work on the case \(\lambda =1\), and Hanani's work on block size 3. The proof relies heavily on the techniques and results of Hanani and Mills, but also includes some new construction techniques based on perturbing the block sets of existing designs.