本项目将利用有限域上的典型群几何学及组合设计等工具研究Pooling设计和压缩感知矩阵的构造以及相关的组合问题。本项目具体研究：基于有限域上典型群作用下的几何空间构造Pooling设计，研究其析取性质。基于有限域上典型群作用下的几何空间构造结合方案，利用所构造的结合方案构造新的Pooling设计，并研究其析取性质。基于有限域上典型群作用下的几何空间构造压缩感知矩阵，分析所构造矩阵恢复信号的能力。

In this project, we will study constructions of pooling designs and compressed sensing matrices and several related topics basing on geometry of classical groups over finite fields, combinatorial designs, etc. The research work of this project will focus on the following aspect: (a) Constructing pooling designs by geometrical spaces under the action of classical groups over finite fields and then discussing its disjunct property. (b) Constructing association schemes by geometrical spaces under the action of classical groups over finite fields and giving a new family of pooling designs by these association schemes. (c) Constructing compressed sensing matrices by geometrical spaces under the action of classical groups over finite fields and analyzing its signal recovery ability.