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In [#!BM:DMFP!#], T. Boykett and P. Mayr established a link from the various sporadic classes of designs built from planar near-rings to the classical theory of designs from difference families. They show that certain sets of fixed-point-free automorphism groups on finite groups form so-called short difference families. Thus they give a general framework to explain the classical designs from near-rings as described by J. Clay and the segments by Sun. Also a new class of BIB-designs with parameters $ (v,k,k(k-1)/2)$ is obtained.

In [#!BM:FAGF!#], T. Boykett and P. Mayr showed that a large class of planar near-rings (Ferrero pairs) is ring-generated. This means that the additive group of the near-ring $ N$ is that of a ring $ R$ and that the multiplication of $ N$ can be obtained by the multiplicative group of $ R$. In this situation planar near-rings and hence designs can be easily obtained from rings.

Peter Mayr 2005-11-25