ABSTRACT
Resolutions of designs have been studied as far back as 1850 by T. P. Kirkman, and since then, designs and resolutions of designs for different parameters have been proven to exist or not exist. In 1986, L. Teirlinck, in his remarkable pioneering paper, proved that simple t-designs exist for all values of t. The central method was actually based on the existence of large sets of t-designs, for arbitrary t, and inspired many mathematicians to find new designs and resolutions. This chapter focuses on a particular family of 2-homogeneous k-semiregular group actions inducing large sets. It aims to create a new family of 2-resolutions, in particular, large sets of 2-designs. The chapter uses the action of the half-affine group on q points to create the family of resolutions. Group actions form a powerful tool in constructing large sets of t-designs.
