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A balanced incomplete Block Design (,
,
,
,
) exists only for
(or, equivalently,
).
See also Bruck-Ryser-Chowla Theorem
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.