Parameters of t-Designs in FPd−1

We derive the subdegrees for a t-design in projective spaces X=FPd−1(F=ℝ,ℂ,ℍ,O). The design may carry an arbitrary finite number of angles. A generalisation of Sidelnikov's inequality is proved and used for this. We give formulae for the parameters of strongly regular graphs that can be realised by a 2 or 3-design carrying two angles, in terms of graph eigenvalues. This leads to a list of feasible parameter sets, some realised