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Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. The theory has applications in the area of the design of experiments.

A combinatorial $t$-$(v,k,\lambda)$ design $D$ is a set of $k$-element subsets of $\{1,\ldots,v\}$ such that each $t$-element subset of $\{1,\ldots,v\}$ is contained in exactly $\lambda$ elements of $D$. Of particular interest are Steiner systems, which are designs with $\lambda = 1$.

This tag should not only be used for narrow sence combinatorial designs, but also for related combinatorial questions like packing designs, covering designs, the spatial arrangement of entries in an array as in Sudoku grids etc.

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