Uniqueness of hypothetical triangle-free strongly regular graphs with given parameters

Determine whether strongly regular graphs with the parameters listed in Table 1.3 (such as (176, 25, 0, 4), (210, 33, 0, 6), (162, 21, 0, 3), (266, 45, 0, 9), (392, 46, 0, 6), (352, 36, 0, 4), (352, 26, 0, 2), (3250, 57, 0, 1))—if they exist—are unique up to isomorphism.

Background

The authors show that any spherical code with the hypothetical parameters in Table 1.3 must arise from a spectral embedding of a strongly regular graph, thereby fixing the structure if such graphs exist.

However, they explicitly note that uniqueness of these graphs (should they exist) is unknown, leaving classification as an open problem.