  This is a report on a failed attempt to construct new graphs that are
strongly regular with no triangles. The approach is based on the assumption
that the second subconstituent has an equitable partition with four parts. For
infinitely many odd prime powers we construct a graph that is a plausible
candidate for the second subconstituent. Unfortuantely we also show that the
corresponding graph is strongly regular only when the prime power is 3, in
which case the graph is already known.
