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][1] which lists all small feasible parameter sets and apparently [this paper][2] shows that $(324,57,0,12)$ is infeasible. 

Is something else known about this problem?


  [1]: http://www.maths.lse.ac.uk/Personal/norman/SRNT.pdf
  [2]: http://onlinelibrary.wiley.com/doi/10.1002/jcd.20145/abstract