PSEUDO GENERALIZED YOUDEN DESIGNS
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Sixty years ago, Kiefer (1958) introduced generalized Youden designs (GYDs) for eliminating heterogeneity in two directions. A GYD is a row-column design whose k rows form a balanced block design (BBD) and whose b columns do likewise. Later Cheng (1981a) introduced pseudo Youden designs (PYDs) in which k = b and where the k rows and the b columns, considered together as blocks, form a BBD. Kiefer (1975a) proved a number of results on the optimality of GYDs. A PYD has the same optimality properties as a GYD. In the present paper, we introduce and investigate pseudo generalized Youden designs (PGYDs) which generalise both GYDs and PYDs. A PGYD is a row-column design where the k rows and b columns, considered together as blocks, form an equireplicate generalized binary variance balanced design. Every GYD is a PGYD and a PYD is exactly a PGYD with k = b. We show, however, that there are situations where a PGYD exists but neither a GYD nor a PYD does. We obtain necessary conditions, in terms of v, k and b, for the existence of a PGYD. Using these conditions, we provide an exhaustive list of parameter sets satisfying v \leq 25; k \leq 50; b \leq 50 for which a PGYD exists. We construct families of PGYDs using patchwork methods based on affine planes.
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