Balanced Semi-Latin Rectangles: Properties, Existence and Constructions for Block Size Two

Abstract

AbstractThere 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.