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There exists no symmetric configuration with 33 points and line size 6. (English) Zbl 1138.05004

Summary: The nonexistence of a symmetric configuration with 33 points and line size 6 is established by means of a point-by-point backtrack search and clique searching. An equivalent result is that there exists no 6-regular bipartite graph with 66 vertices and girth 6. Combining with earlier results, it is now known that a symmetric configuration with line size 6 exists if and only if the number of points is 31 or at least 34. A further result obtained with essentially the same approach is that there exists no symmetric 2-configuration with 23 points and line size 7.

MSC:

05B05 Combinatorial aspects of block designs
05B30 Other designs, configurations

Software:

nauty
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