Table of Contents
International Journal of Combinatorics
Volume 2010 (2010), Article ID 821078, 14 pages
http://dx.doi.org/10.1155/2010/821078
Research Article

On Symmetric Transversal Designs STD8[24; 3]'s

Department of Mathematics, Faculty of Engineering, Oita University, Oita 870-1192, Japan

Received 20 January 2010; Accepted 17 March 2010

Academic Editor: Laszlo A. Szekely

Copyright © 2010 Teppei Hatono and Chihiro Suetake. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Kimura, “Classification of Hadamard matrices of order 28,” Discrete Mathematics, vol. 133, no. 1–3, pp. 171–180, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. V. C. Mavron and V. D. Tonchev, “On symmetric nets and generalized Hadamard matrices from affine designs,” Journal of Geometry, vol. 67, no. 1-2, pp. 180–187, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. C. Suetake, “The classification of symmetric transversal designs STD4[12;3]'s,” Designs, Codes and Cryptography, vol. 37, no. 2, pp. 293–304, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  4. W. H. Haemers, “Conditions for singular incidence matrices,” Journal of Algebraic Combinatorics, vol. 21, no. 2, pp. 179–183, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. W. de Launey, A personal communication.
  6. W. de Launey, (0,G)-designs with applications, Ph.D. thesis, University of Sydney, Sydney, Australia, 1987.
  7. Y. Zhang, L. Duan, Y. Lu, and Z. Zheng, “Construction of generalized Hadamard matrices D(rm(r+1),rm(r+1);p),” Journal of Statistical Planning and Inference, vol. 104, no. 2, pp. 239–258, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. K. Akiyama and C. Suetake, “The nonexistence of projective planes of order 12 with a collineation group of order 8,” Journal of Combinatorial Designs, vol. 16, no. 5, pp. 411–430, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. Suetake, “Automorphism groups of a symmetric transversal design STD2[12;6],” Journal of Statistical Theory and Practice, vol. 3, pp. 429–443, 2009. View at Google Scholar
  10. T. Beth, D. Jungnickel, and H. Lenz, Design Theory, Volumes I and II, Cambridge University Press, Cambridge, UK, 1999.
  11. C. J. Colbourn and J. H. Dinit, Eds., Handbook of Combinatorial Designs, Discrete Mathematics and Its Applications, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2nd edition, 2007. View at MathSciNet
  12. Y. J. Ionin and M. S. Shrikhande, Combinatorics of Symmetric Designs, vol. 5 of New Mathematical Monographs, Cambridge University Press, Cambridge, UK, 2006. View at MathSciNet
  13. V. D. Tonchev, Combinatorial Configurations: Designs, Codes, Graphs, vol. 40 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1988. View at MathSciNet
  14. K. Akiyama and C. Suetake, “On STDk/3[k;3]'s,” Discrete Mathematics, vol. 308, no. 24, pp. 6449–6465, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  15. K. Akiyama, M. Ogawa, and C. Suetake, “On STD6[18,3]'s and STD7[21,3]'s admitting a semiregular automorphism group of order 9,” The Electronic Journal of Combinatorics, vol. 16, pp. 1–21, 2009. View at Google Scholar