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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.

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Covering designs where $v$ is linear in $k$

A $(v,k,t)$ covering design is a collection of $k$-subsets of $V=\{1,\ldots,v\}$ chosen so that any $t$-subset of $V$ is contained in (or "covered by") at least one $k$-set in the collection. Existen …
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