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.

Hadamard matrix | symmetric block design

Jacques Hadamard