The Challenge of Generating Spatially Balanced Scientific Experiment Designs

The development of the theory and construction of combinatorial designs originated with the work of Euler on Latin squares. A Latin square on n symbols is an n × n matrix (n is the order of the Latin square), in which each symbol occurs precisely once in each row and in each column. Several interesting research questions posed by Euler with respect to Latin squares, namely regarding orthogonality properties, were only solved in 1959 [3]. Many other questions concerning Latin squares constructions still remain open today.

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