This thesis is concerned with the study of Delsarte designs in symmetric association schemes, particularly in the context of finite geometry. We construct an infinite family of hemisystems of the parabolic quadrics Q(2d, q) for q an odd prime power, and d at least 2. We consider how one might constrain the strata or the size of a design using Krein parameters, and explore the construction of "witnesses" to the non-existence of designs. We show that m-ovoids of certain regular near polygons must be hemisystems. We also introduce strong semi-canonicity for more efficient computation, and obtain various new computational results.
|Qualification||Doctor of Philosophy|
|Award date||15 Dec 2020|
|Publication status||Unpublished - 2020|