Generalized quadrangles with a regular point and association schemes

AbstractThere is a new method of constructing generalized quadrangles (GQs) which is based on covering of nets; all GQs with a regular point can be represented in this way. Here we first construct from a generalized quadrangle Q with a regular point a four-class association scheme A(Q) called in brief geometric. It is then natural to call pseudo-geometric any association scheme A with the same parameters as A(Q). We use eigenvalue techniques and the above method of construction to give a characterization of pseudo-geometric association schemes which are geometric