# Interpreting in higher dimensions with maximal spacing

I have data that I would like to interpret in higher dimension (sort of the opposite of an auto-encoder). What I intent to achieve is, an m dimension data being represented in n dimensions (n>m) with the constraint that the representation in the n dimensions is maximally separated.

For clarity, I will assume the binary field. My data has m=20 dimensions. I would like to represent this data in a n=50 dimensional space. There are 2^m number of data combinations that are possible and 2^n number of points in the larger dimension. My goal is to select 2^m points from 2^n points, which are as far away from each other as possible.

I am versed with neural networks. What I want to know is how do I tackle this problem from a neural network perspective? Thanks!