Nonabelian groups of order 100, that are extensions of the elementary abelian group E 25 by the group Z 4 are considered as possible automorphism groups of symmetric designs with parameters (100, 45, 20). By the action of these groups new (100, 45, 20) symmetric designs are constructed. Their full automorphism groups are given.
The correspondence between a (96, 20, 4) symmetric design having regular automorphism group and a difference set with the same parameters has been used to obtain difference sets in groups of order 96. Starting from eight such symmetric designs constructed by the tactical decomposition method, 55 inequivalent (96, 20, 4) difference sets are distinguished.… (More)
New (96,20,4,4) and (96,19,2,4) regular partial difference sets are constructed, together with the corresponding strongly regular graphs. Our source are (96,20,4) regular symmetric designs.