CAs

Creates covering arrays.

• Author: Ulrike Groemping, BHT Berlin.

• License: GPL-3

Warning

This is a very preliminary version of R package CAs. Changes that break backwards compatibility can and will occur without warning.

Installation

CAs is not yet on CRAN. If you want to work with this very preliminary version (see above warning), you can install the package from this repository with:

if (!require(devtools)) install.packages("devtools")
devtools::install_github("ugroempi/CAs")

Details

This package constructs covering arrays, i.e., arrays that cover all $t$-ary combinations of a set of factors at least once. The focus is on mathematical constructions. Initially, the package only offers arrays for which all columns have the same number of levels.

The goal is to implement as many constructions as possible that yield arrays with small numbers of runs, as evidenced by the Colbourn covering array tables, which do not provide the CAs themselves but pointers to which CA constructions yield the smallest known array for which setting.

All references of the package are listed in this file and referenced from the other documentation files.

Within the package, available CA constructions for specific situations can be queried using the guide functions guide_CAs (not yet implemented, might be changed).

Besides the construction functions, coverage properties of any array can be checked by function coverage and plotted by function coverplot.

So far, constructions for strength 2 2-level CAs by Kleitman and Spencer (1973) and Katona (1973), as well as constructions based on cyclotomy (Colbourn 2010) have been implemented.

References

The Colbourn tables are currently unavailable at their usual location; temporarily, access is provided here.

Ball, W. W. R. and Coxeter, H. S. M. (1987). Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 308-309.

Chateauneuf, M. and Kreher, D.L. (2002). On the state of strength‐three covering arrays. Journal of Combinatorial Designs, vol. 10, no. 4, pp. 217-238. doi: 10.1002/jcd.10002.

Colbourn, C.J. (without year). Covering array tables: 2 ≤v ≤25, 2 ≤t≤6, t≤k ≤10000, 2005–23. https://www.public.asu.edu/~ccolbou/src/tabby.

Colbourn, C. J. (2010). Covering arrays from cyclotomy, Des. Codes Cryptogr., vol. 55, no. 2, pp. 201–219. doi: 10.1007/s10623-009-9333-8.

Kleitman, D.J. and Spencer, J. (1973). Families of k-independent sets, Discrete Math., vol. 6, no. 3, pp. 255–262. doi: 10.1016/0012-365X(73)90098-8.

Katona, G. O. H. (1973). Two applications (for search theory and truth functions) of Sperner type theorems, Period. Math. Hung., vol. 3, no. 1, pp. 19–26. doi: 10.1007/BF02018457.

Martirosyan, S. and Trung, T.V. (2004). On t-Covering Arrays. Des. Codes Cryptogr., vol. 32, no. 2, pp. 323–339. doi: 10.1023/B:DESI.0000029232.40302.6d.

NIST Covering Array Tables (last modified 2008, accessed 12 Jan 2025). https://math.nist.gov/coveringarrays/.

Torres-Jimenez, J. (without year, accessed 10 Feb 2025). Covering arrays. https://www.tamps.cinvestav.mx/~oc/.

Zhang, J., Zhang, Z. and Ma, F. (2014). Automatic Generation of Combinatorial Test Data. SpringerBriefs in Computer Science. Springer Verlag, Berlin.