Geometry has always been a central part of mathematics.

Clay first observed that the usual Euclidean geometry of the
complex plane can be obtained using a double planar nearring structure
imposed on it. This was done by first factoring the multiplicative group
of the complex field as the direct product of the positive reals and the
unit circle, and two planar nearring structures were obtained. Then using
these planar nearrings he defined rays, segments and triangles using one
of the nearrings and circles using the other. These geometric results can
be extended to other fields, including finite fields, where the
multiplicative group can be suitably factored.

A finite incidence structure is sometimes also called a (finite)
geometric structure. It is the most basic structure of the
design theory.
The projective and affine geometries of finite-dimensional vector spaces over
finite fields provide the deepest source for the theory of designs.
In fact, they are two ways of constructing $2$-design.

Designs are usually classified by their parameter sets, by their
membership of infinite families, or according to the type of automorphism
group they admit --- or in other ways related to their geometric
properties.

In this dissertation we will first review some basic results in planar
nearrings and blocks designs, and then review how to construct a block
design from a planar nearring. We will also give a survey on the geometric
properties of planar nearrings and block designs.
Finally, we will describe the full automorphism group
of certain simple $2$-$(v,3,lambda)$ designs which arise from
some geometrical consideration.

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ibitem{CamSie}
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