Balanced semi-Latin rectangles : properties, existence and constructions for block size two
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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 concur 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 (BSLR) 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.
Uto , N P & Bailey , R A 2020 , ' Balanced semi-Latin rectangles : properties, existence and constructions for block size two ' , Journal of Statistical Theory and Practice , vol. 14 , no. 3 , 51 . https://doi.org/10.1007/s42519-020-00118-3
Journal of Statistical Theory and Practice
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