{0,2,4}-semiaffine planes

A {0,2,4} -semiaffine plane is defined to be a linear space in which (a) for any point p and nonincident line l the number of lines through p that miss l is 0, 2, or 4, and (b) for each of these numbers there exists at least one such point-line pair. The authors classify two subclasses of finite {0,2,4} -semiaffine planes: those in which not all points contain the same number of lines, and those in which every point contains the same number of lines while one of those points contains all the lines of minimum cardinality.