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Balanced semi-Latin rectangles: properties, existence and constructions for block size two. (English) Zbl 1456.62162

Summary: There exists a set of designs which form a subclass of semi-Latin rectangles. These designs, besides being semi-Latin rectangles, exhibit an additional property of balance, where no two distinct pairs of symbols (treatments) differ in their concurrences, that is, each pair of distinct treatments concurs a constant number of times in the design. Such a design exists for a limited set of parameter combinations. We designate it a balanced semi-Latin rectangle and give some properties and necessary conditions for its existence. Furthermore, algorithms for constructing the design for experimental situations where there are two treatments in each row-column intersection (block) are also given.

MSC:

62K10 Statistical block designs
05B15 Orthogonal arrays, Latin squares, Room squares
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