It's hard to imagine, and it seems that this topic has little to do with my own research, but I have to understand and compare it through experiments as a basis to support the algorithm theory of the paper. All day, my brain seems to be spinning around the "hyper sphere" and "hyper cube" in a panic, but I still can't understand the mystery. In fact, what are n-dimensional hyperspheres and hypercubes? Who can tell me? Nobody can. The human brain can't imagine and perceive things above three dimensions, and can only simulate and display things above three dimensions at most. In this way, from the perspective of ordinary people, it is a bit abnormal for us to do research and think about these eternal problems. Although I can't understand the mystery for the time being, I will definitely learn something from it. First of all, I know some theoretical formulas that I have never thought or imagined, and related theoretical analysis. In particular, what Google stumbled upon verified the correctness of the symbolic computing course chosen last semester. At least know a powerful mathematical processing software-Mathematica, and its manual notes, which bring together hundreds of essences, from which we can find extremely rich mathematical knowledge. For example, the detailed introduction and handling methods of this hyper-sphere and hyper-cube come from its online notes. Secondly, we have obtained some useful resources, such as the online encyclopedia of integer sequences, which are classified into books according to integer sequences. The description of all kinds of knowledge is concise and intuitive, and it can be said that everything is available. :-(