Construction of Generalized Cyclic Combinatorially Balanced Designs for First Order Residual Treatment Effects

Abstract

Designs combioatorially balanced for residual treatment effects of various orders, (especialJy first and second orders) with and without interactions were discussed in considerable details by williams (1949). Construction of combinatorially balanced designs for residual treatment effects was also considered by Patterson (1952); Hedayat and Afsarinejad (1975, 1978); Cheng and Wu (1980). An excellent account of such designs is given by Jones and Kenward (1989).

In this paper, a method of construction of generalized cyclic designs combinatorially balanced for residual treatment effects of the first order without interactions, is presented. The method is based on an extension of theorems on symmetricaliy repeated difference sets developed by Bose (1939) and others. See Raghavarao (1971) for deiails,

AMS (1980) Subject Classification: Primary 62k99; Secondary 05B10,05B30