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# Brock TR # CS-00-04 Abstract

*The Search for a (46, 6, 1) Block Design * [PDF]

S.K. Houghten, L.H. Thiel, J. Janssen, and C.W.H. Lam, November 2000.

In this paper we report the results of a computer search for a (46,6,1) block design. In the incidence matrix of such a design, there must exist a "c4" configuration - 6 rows and 4 columns, in which each pair of columns intersect exactly once, in distinct rows. There can also exist a "c5" configuration - 10 rows and 5 columns, in which each pair of columns intersect exactly once, in distinct rows. Thus the search for (46,6,1) designs can be subdivided into two cases, the first of which assumes there is no "c5", and the second of which assumes there is a "c5". After completing the searches for both cases, we found no (46,6,1) design.