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.
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© 1996 Springer Science+Business Media Dordrecht
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McKay, B.D., Radziszowski, S.P. (1996). The Nonexistence of 4-(12,6,6) Designs. In: Wallis, W.D. (eds) Computational and Constructive Design Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2497-4_7
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DOI: https://doi.org/10.1007/978-1-4757-2497-4_7
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