On the Existence of Strong Kirkman Cubes of Order 39 and Block Size 3

In this article we are interested in resolvable (v,k,1)-BIBDs. Let D be a (v,k,1)-BIBD and let R and S be two resolutions of the blocks of D. R and S are said to be orthogonal resolutions if any parallel class from R has at most one block in common with any class of S. A set of t resolutions of D is called a set of t orthogonal resolutions if every pair of these resolutions is orthogonal. For t = 2 the design resulting is called a Kirkman …