A Symmetric Block Design (, , ) which is equivalent to a Hadamard Matrix of order . It is conjectured that Hadamard designs exist for all integers , but this has not yet been proven. This elusive proof (or disproof) remains one of the most important unsolved problems in Combinatorics.
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.