Hadamard Design

A Symmetric Block Design ($4n+3$, $2n+1$, $n$) which is equivalent to a Hadamard Matrix of order $4n+4$. It is conjectured that Hadamard designs exist for all integers $n>0$, but this has not yet been proven. This elusive proof (or disproof) remains one of the most important unsolved problems in Combinatorics.

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.