Orthogonal Resolutions in Odd Balanced Tournament Designs

An odd balanced tournament design,OBTD(n), is ann × 2n + 1 array of pairs defined on a (2n + 1)-setV such that (1) every row of the array contains each element ofV twice, (2) every column of the array contains 2n distinct elements ofV, and (3) the pairs of the array form a (2n + 1, 2, 1)-BIBD. In this paper, we investigate the spectrum of odd balanced tournament designs with orthogonal resolutions. These designs can be used to construct doubly near resolvable (v, 3, 2)-BIBDs.