An algorithm for constructing Hjelmslev planes

Projeclive Hjelmslev planes and affine Hjclmslev planes are generalisations of projective planes and affine planes. We present an algorithm for constructing projeclive Hjelmslev planes and affine Hjelmslev planes that uses projective planes, affi ne planes and orthogonal arrays. \Ve show that all 2-uniform projective Hjelmslev planes and all 2-uniform affine Hjelmslev planes can be constructed in this way. As a corollary it is shown that all 2-unifonn affine Hjelmslev planes arc sub-geometrics of 2-uniform projective Hjclmslcv planes