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

  • Brendan D. McKay
  • Stanisław P. Radziszowski


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.


Automorphism Group Design Theory Partial Design Steiner System Related Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Brendan D. McKay
    • 1
  • Stanisław P. Radziszowski
    • 2
  1. 1.Department of Computer ScienceAustralian National UniversityCanberraAustralia
  2. 2.Department of Computer ScienceRochester Institute of TechnologyRochesterUSA

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