Kaski, Petteri; Östergård, Patric R. J. There exists no symmetric configuration with 33 points and line size 6. (English) Zbl 1138.05004 Australas. J. Comb. 38, 273-277 (2007). 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. Reviewer: Corrado Zanella (Padova) Cited in 4 Documents MSC: 05B05 Combinatorial aspects of block designs 05B30 Other designs, configurations Keywords:symmetric configuration; symmetric block design; regular bipartite graph Software:nauty PDFBibTeX XMLCite \textit{P. Kaski} and \textit{P. R. J. Östergård}, Australas. J. Comb. 38, 273--277 (2007; Zbl 1138.05004)