Derivation of m-systems

AbstractWe will discuss a way to construct new m-systems from known ones by replacing a number of elements of the m-system by a set of other subspaces covering the same points. Further, we investigate in which cases this method can be applied and we find new classes of 1-systems. In the last section, the semipartial geometries arising from 1-systems of W5(q) are studied and it is shown that some of the new 1-systems we have found yield new semipartial geometries