Replaceable Nets, Net Collineations, and Net Extensions

Abstract

A net of degree k and order n is a set of n² points and nk designated sets of points, called lines, such that (1) The lines fall into k disjoint parallel classes, i.e. each line occurs in exactly one parallel class. (2) Lines in the same parallel class have no points in common; lines in different parallel classes have exactly one point in common. (3) Each point lies on exactly one line of each parallel class.