Configurations and \((r,1)\)-designs. (English) Zbl 0801.05017
The author examines the links between \((r,1)\)-designs, i.e., linear spaces in which each point lies on \(r\) lines, and \((v_ r,b_ k)\)- configurations and constructs all \((r,1)\)-designs with at most 12 points. (There are 974 of these and most of them are \((v_ r,b_ k)\)- configurations.) The designs are constructed by using the possible geometric structures they can have and this is achieved by considering the possible point types. The type of a point is defined as the set of numbers of lines of different sizes through it. Links with graphs are exploited, too.
Reviewer: M.J.De Resmini (Roma)
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