Existence results for generalized balanced tournament designs with block size 3

A generalized balanced tournament design,GBTD(n, k) defined on akn-setV, is an arrangement of the blocks of a (kn, k, k–1)-BIBD defined onV into ann× (kn–1), array such that (1) every element ofV is contained in precisely one cell of each column, and (2) every element ofV is contained in at mostk cells of each row. In this paper, we completely determine the spectrum ofGBTD(n, 3). In addition we prove the exitence of factoredGBTD(n, 3) forn a positive integer,n4, with at most one possible exception.This research was supported by a Postdoctoral membership at the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455.