Skip to main content
Log in

Covering Arrays of Strength Three

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

A covering array of size N, degree k, order v and strength t is a k × N array with entries from a set of v symbols such that in any t × N subarray every t × 1 column occurs at least once. Covering arrays have been studied for their applications to drug screening and software testing. We present explicit constructions and give constructive upper bounds for the size of a covering array of strength three.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Atici, S. S. Magliveras, D. R. Stinson, and W.-D. Wei, Some recursive constructions for perfect hash functions, J. Combinat. Designs, Vol. 4 (1996) pp. 353-363.

    MathSciNet  Google Scholar 

  2. D. M. Cohen, S. R. Dalal, M. L. Fredman, and G. C. Patton, The AETG system: an approach to testing software based on combinatorial design, IEEE Trans. Software Engineering, Vol. 23 (1997) pp. 437-444.

    Google Scholar 

  3. D. M. Cohen, S. R. Dalal, J. Parelius, and G. C. Patton, The combinatorial design approach to automatic test generation, IEEE Software, Vol. 13 (1996) pp. 83-88.

    Article  Google Scholar 

  4. C. J. Colbourn and J. H. Dinitz, editors, The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton (1996).

    Google Scholar 

  5. C. J. Colbourn and D. L. Kreher, Concerning difference matrices, Designs, Codes and Cryptography, Vol. 9 (1996) pp. 61-70.

    MathSciNet  Google Scholar 

  6. L. Gargano, J. Körner, and U. Vaccaro, Sperner capacities, Graphs and Combinatorics, Vol. 9 (1993) pp. 31-46.

    Article  MathSciNet  Google Scholar 

  7. A. P. Godbole, D. E. Skipper, and R. A. Sunley, t-Covering arrays: upper bounds and Poisson approximations, Combinatorics, Probability and Computing, Vol. 5 (1996) pp. 105-118.

    MathSciNet  Google Scholar 

  8. J. Körner and M. Lucertini, Compressing inconsistent data, IEEE Trans. Information Theory, Vol. 40 (1994) pp. 706-715.

    Google Scholar 

  9. D. L. Kreher, Orthogonal arrays of strength 3, J. Combinat. Designs, Vol. 4 (1996) pp. 67-69.

    MATH  MathSciNet  Google Scholar 

  10. S. Poljak, A. Pultr, and V. Rödl, On qualitatively independent partitions and related problems, Discrete Applied Math., Vol. 6 (1983) pp. 193-205.

    Article  Google Scholar 

  11. N. J. A. Sloane, Covering arrays and intersecting codes, J. Combinat. Designs, Vol. 1 (1993) pp. 51-63.

    MATH  MathSciNet  Google Scholar 

  12. B. Stevens and E. Mendelsohn, New recursive methods for transversal covers, J. Combinat. Designs, to appear.

  13. A.-I. Tong, Y.-G. Wu, and L.-D. Li, Room-temperature phosphorimetry studies of some addictive drugs following dansyl chloride labelling, Talanta, Vol. 43 (1996) pp. 1429-1436.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chateauneuf, M.A., Colbourn, C.J. & Kreher, D.L. Covering Arrays of Strength Three. Designs, Codes and Cryptography 16, 235–242 (1999). https://doi.org/10.1023/A:1008379710317

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008379710317

Navigation