Pseudo generalized Youden designs. Issue 9 (20th November 2017)

• Record Type: Journal Article
• Authors: Das, Ashish; Horsley, Daniel; Singh, Rakhi
• Is Part Of: Journal of combinatorial designs. Volume 26:Issue 9(2018:Sep.)
• Page Start: 439
• Page End: 454
• Publication Date: 2017-11-20
• Subjects: balanced block design -- generalized Youden design -- pseudo Youden design -- Youden square design; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21594
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: Youden square designs, or Youden rectangles, are classical objects in design theory. Extensions of these were introduced in 1958 by Kiefer and in 1981 by Cheng, in the form of generalized Youden designs (GYDs) and pseudo Youden designs (PYDs), respectively. In this paper, we introduce a common generalization of both these objects, which we call a pseudo generalized Youden design (PGYD). PGYDs share the statistically desirable optimality properties of GYDs and PYDs, and we show that they exist in situations where neither GYDs nor PYDs do. We determine some numerical necessary conditions for the existence of PGYDs, classify their existence for small parameter sets, and provide constructions for families of PGYDs using patchwork methods based on affine planes.