imagine a two dimensional plane inhabited by two dimensional creatures
we will call it flatland
now imagine an infinite number of squares in flatland
the flatlanders want to store all the squares in a compact space but there are to many squars to do that!
however they have discovered the third dimension so they stack all the infinite squares into a cube in the third dimension
now there all stored in a small compact space
in or world if we had an infinite number of cubes we could stack them in the fourth dimension and make a tesseract to store them all compactly
the more dimensions we have the more compactly we can story materials!
so in an infinite dimensional space we can store a really small particle in one dimension and another particle in another dimension and store an infinite amount of materials in an extremely small space!
as we have seen above we dont even need infinite dimensions to store an amount of materials in a finite amount of space!