A simple replacement approach is used to construct new symmetric and affine designs from projective or affine spaces. This is used to construct symmetric designs with a given automorphism group, to study GMW designs, and to construct new affine designs whose automorphism group fixes a point and has just two point- and block-orbits. Keywords Symmetric and affine designs ? Projective or affine spaces ? GMW designs ? Point- and block-orbits AMS Classifications 05B05 ? 05B25 ? 51E05 ? 05B10
Ulrich Dempwolff, William M. Kantor