$\mathcal{P}$ called blocks. Designs serve as a fundamental tool to investigate combinatorial objects. Also designs have attracted many researchers from different fields for solutions of applications problems including binary sequences with $2$-level autocorrelation, optical orthogonal codes, low density parity check codes, synchronization, radar, coded aperture imaging, and optical image alignment, distributed storage systems and cryptographic functions with high nonlinearity[@chung1989; @delsarte; @dillon1974; @ding2015; @olmez2].

One of the main construction method of designs is called difference set method. This method served as a powerful tool to construct symmetric designs, error correcting codes, graphs and cryptographic functions [@assmus1992; @bernasconi2001; @bjl; @brouwer2012; @buratti2011; @dingbook; @dingbook2; @pott; @pott2011]. This paper will focus on the links between designs and a family of a function known as plateaued functions from cryptography. Especially we will investigate the connections between partial geometric difference sets and graph of plateaued functions.

A function from the field $\mathbb{F}_{p^{n}}$ to $\mathbb{F}_p$ is called a $p$-ary function. If $p=2$ then the function is simply called as Boolean. $p$-ary functions with various characteristics have been an active research subject in cryptography. Bent functions and plateaued functions are two well-known families which has prominent properties in this field [@carlet2003; @CCC; @Carlet; @Carlet1; @Carlet2; @CarM; @Mes1; @Mes2]. 