A symmetric design is a Block Design (, , , , ) with the same number of blocks as points, so (or, equivalently, ). An example of a symmetric block design is a Projective Plane.
See also Block Design, Projective Plane
References
Dinitz, J. H. and Stinson, D. R. ``A Brief Introduction to Design Theory.'' Ch. 1 in
Contemporary Design Theory: A Collection of Surveys (Ed. J. H. Dinitz and D. R. Stinson).
New York: Wiley, pp. 1-12, 1992.