A balanced incomplete block design (
, 
, 
, 
, 
) exists only for 
(or, equivalently, 
).
Fisher's Block Design Inequality
See also
Bruck-Ryser-Chowla TheoremExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Fisher's Block Design InequalityCite this as:
Weisstein, Eric W. "Fisher's Block Design Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FishersBlockDesignInequality.html