New \(t\)-designs and large sets of \(t\)-designs
The authors report the results of their computer-aided search for simple \(t\)-\((v,k,\lambda)\) designs and large sets of designs. The main tool used in their search is the computer program DISCRETA developed by the authors and based on the method of Kramer and Mesner [see \textit{E. S. Kramer} and \textit{D. M. Mesner}, Discrete Math. 15, 263-296 (1976; Zbl 0362.05049)] further combined with some previously known recursive methods. The paper provides a brief list of the recursive methods used and a short description of the use of DISCRETA (which allows one to choose the automorphism group for the prospective design, and appears to be rather user friendly). A table of all the presently known simple \(t\)-\((v,k,\lambda)\) designs, \(t\geq 7\) and \(v\leq 40\), is included (most of them found by the authors) as well as several results on the existence of infinite families of large sets of \(t\)-designs.
scientific article; zbMATH DE number 1322004