Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries

@article{Kung1988CombinatorialGR,
title={Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries},
author={Joseph P. S. Kung and James G. Oxley},
journal={Graphs and Combinatorics},
year={1988},
volume={4},
pages={323-332}
}

Let q be an odd prime power not divisible by 3. In Part I of this series, it was shown that the number of points in a rank-n combinatorial geometry (or simple matroid) representable over GF(3) and GF(q) is at most n z. In this paper, we show that, with the exception of n = 3, a rank-n geometry that is representable over GF(3) and GF(q) and contains exactly n z points is isomorphic to the rank-n Dowling geometry based on the multiplicative group of GF(3).