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The study of Designs and, in particular, Necessary and Sufficient conditions for the existence of a Block Design.
See also Bruck-Ryser-Chowla Theorem, Fisher's Block Design Inequality
References
Assmus, E. F. Jr. and Key, J. D. Designs and Their Codes. New York: Cambridge University Press, 1993.
Colbourn, C. J. and Dinitz, J. H. CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, 1996.
Dinitz, J. H. and Stinson, D. R. (Eds.). ``A Brief Introduction to Design Theory.'' Ch. 1 in
Contemporary Design Theory: A Collection of Surveys. New York: Wiley, pp. 1-12, 1992.