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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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Orthogonal Latin Square 6*6
A modern account of the problem (including an interesting way of solving it) can be found in this paper by Steven Dougherty:
http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co …