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The Nonexistence of 4-(12,6,6) Designs

In: Computational and Constructive Design Theory

Author

Listed:
  • Brendan D. McKay

    (Australian National University, Department of Computer Science)

  • Stanisław P. Radziszowski

    (Rochester Institute of Technology, Department of Computer Science)

Abstract

With the help of computer algorithms we prove that there are no 4-(12, 6, 6) designs, thereby answering the last open existence question in design theory for at most 12 points. We also enumerate three families of related designs, namely the 10977 simple 3-(10, 4, 3) designs, the 67 simple 4-(11, 5, 3) designs, and the 23 simple 5-(12, 6, 3) designs. Finally, we complete the census of all possible partitions of 6-sets on 12 points into 5-(12, 6, A) designs and of 5-sets on 11 points into 4-(11, 5, A) designs.

Suggested Citation

  • Brendan D. McKay & Stanisław P. Radziszowski, 1996. "The Nonexistence of 4-(12,6,6) Designs," Springer Books, in: W. D. Wallis (ed.), Computational and Constructive Design Theory, chapter 0, pages 177-188, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-2497-4_7
    DOI: 10.1007/978-1-4757-2497-4_7
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