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

Brendan D. McKay () and Stanisław P. Radziszowski ()
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Brendan D. McKay: Australian National University, Department of Computer Science
Stanisław P. Radziszowski: Rochester Institute of Technology, Department of Computer Science

Chapter Chapter 7 in Computational and Constructive Design Theory, 1996, pp 177-188 from Springer

Abstract: 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.

Keywords: Automorphism Group; Design Theory; Partial Design; Steiner System; Related Design (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4757-2497-4_7

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