Two existence results between an affine resolvable SRGD design and a difference scheme

Abstract

A bstract . The existence of a‰ne resolvable block designs has been discussed since 1942 in the literature (cf. Bose (1942), Clatworthy (1973), Raghavarao (1988)). Kadowaki and Kageyama (2009, 2010, 2012) obtained a number of results on combinatorics for the existence of an a‰ne resolvable SRGD design. In this paper, a new existence result is shown as a generalization of Theorem 3.3.3 given in Kadowaki and Kageyama (2009, 2010). Furthermore, another existence result is shown as a conditional converse of Theorem 3.3.3 and also a generalization of Theorem 3.3.4, both theorems given in Kadowaki and Kageyama (2009, 2010).