Designs Obtained from Affine Spaces

Abstract

Publisher Summary This chapter presents some geometric constructions of designs (BIB-designs) and designs with parallelism obtained in affine spaces. By these methods some classes of affine designs are determined that are not affine spaces and some special designs called calibration designs. The chapter describes two constructive methods of obtaining designs from affine spaces. The first method makes use of a property possessed by affine spaces—two-transitivity—and gives infinite classes of designs. Using the second method other designs with parallelism from affine spaces can be derived. The main characteristic of designs obtained is their geometrical structure. Some of them have the further property of being applicable to situations of special interest—for example, some designs shown in the chapter with even block size may be used as “calibration designs.” These are designs where blocks can be partitioned into smaller blocks of a design on the same point set—that is, one obtains a refinement of the given design.