The combinatorial (19_4) configurations

Abstract

A parallel backtrack search is carried out to classify, up to isomorphism, all combinatorial (19₄) configurations. A total of 269 224 652 such configurations were found. We prove that two of the combinatorial (19₄) configurations are not geometrically realizable over any field. Also we confirmed the computation of the 971 171 combinatorial (18₄) configurations which lacked an independent verification.