Covering arrays and intersecting codes

N. J. A. Sloane
1993 Journal of combinatorial designs (Print)  
A t-covering array is a set of k binary vectors of length n with the property that, in any t coordinate positions, all 2t possibilities occur at least once. Such arrays are used for example in circuit testing, and one wishes to minimize k for given values of n and t. The case t = 2 was solved by Rknyi, Katona, and Kleitman and Spencer. The present article is concerned with the case t = 3, where important (but unpublished) contributions were made by Busschbach and Roux in the 1980s. One of the
more » ... incipal constructions makes use of intersecting codes (linear codes with the property that any two nonzero codewords meet). This article studies the properties of 3-covering arrays and intersecting codes, and gives a table of the best 3-covering arrays presently known. For large n the minimal k satisfies 3.21256 < k / log n < 7.56444. 01993 John Wiley & Sons, Inc.
doi:10.1002/jcd.3180010106 fatcat:fzaevcbqsrbzfp6gvgcxswfzpm