Quasi-symmetric 2-designs

TL;DRAbstract

In our earlier chapters, we have looked at various classes of (sometimes only parametrically possible) quasi-symmetric designs. This chapter is devoted to the study of quasi-symmetric designs in general, particularly from a structural point of view. While Cameron's Theorem (Theorem 1.29) certainly boosted the interest in quasi-symmetric designs, it seems to be only in the last ten years or so that the structural investigations of quasi-symmetric designs began. The investigations are far from complete and we wish to give an account of the work in this area. The strong regularity of the block graph of a q.s. (= quasi-symmetric) design has been exploited in a paper of Neumaier. However, the design-structural properties of q.s. designs were probably first studied in a paper of Baartmans and M.S. Shrikhande. In that paper, q.s. designs with (x, y) = (0, y), y ≥ 2 and with no three mutually disjoint blocks were studied. Typical examples are Eλ and Qλ of Chapter VII (Convention 7.12). Various

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