On a characterization of T-designs

This thesis is an exposition of Sylvia Hobart\u27s article On a Characterization of t-designs in terms of the Inner Distribution. An inequality for o-designs is derived which holds with equality, if and only if the design is a t-design where o is less than or equal to t less than or equal to k. This inequality is then applied to the case of regular designs that is designs in which the number of blocks intersecting a given block in a given number of points is a constant. This analysis is used to characterize the Steiner system S-(4,7,23) in terms of the derived design at two points. A thorough discussion on designs as well as the details of the proofs found in Hobart\u27s article are presented in this thesis. Examples are constructed for better understanding