What is the state of the art on triangle-free strongly regular graphs?

From what I've read I've gathered the following facts:

• There are seven known such graphs.
• Certain parameter sets are ruled out by the Krein conditions and the absolute bound.
• Beyond that, little or nothing is known.

Am I missing something? I have read Biggs's report which lists all small feasible parameter sets and apparently this paper shows that (324,57,0,12) is infeasible.

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The complete bipartite graphs $K_{n,n}$ are strongly regular and triangle-free. This nitpicking aside, your summary is accurate.