On topological and geometric [formula omitted] configurations.

An ( n k ) configuration is a set of n points and n lines such that each point lies on k lines while each line contains k points. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. The existence and enumeration of ( n k ) configurations for a given k has been subject to active research. A current front of research concerns geometric ( n 4 ) configurations: it is now known that geometric ( n 4 ) configurations exist for all n ≥ 18 , apart from sporadic exceptional cases. In this paper, we settle by computational techniques the first open case of ( 1 9 4 ) configurations: we obtain all topological ( 1 9 4 ) configurations among which none are geometrically realizable. [ABSTRACT FROM AUTHOR]