3-Designs from ${\mathrm{GL}}_2({\mathbb{F}}_q)$-Invariant Subspaces of ${\mathbb{F}}_q[X,Y{]}_k$

Lewen Wang, Huawei Wu, Sihuang Hu

We present a uniform framework for constructing $3$-designs from ${\mathrm{GL}}_2({\mathbb{F}}_q)$-invariant subspaces of ${\mathbb{F}}_q[X,Y{]}_k$, the space of homogeneous polynomials of d…