| Abstract: | The article is concerned with a characterization of quasi-symmetric (QS) designs with intersection numbers 0 and y. It uses the idea of a good block. Such a block G has the property that for any block B with |G ∩ B| = y, every point is on a block containing G ∩ B. It is proved that if a QS design II with intersection numbers 0 and y has a good block, then II must (i) be affine, symmetric, a linear space or (ii) have one of two possible exceptional parameter sets. Only one example is known in case (ii). If all blocks of II are good and II is not a linear space, then it is a projective or affine geometry or it is an extension (in a more general sense than usual) of a projective plane of order y2 or y3+ y. © 1995 John Wiley & Sons, Inc. |
