A geometry of space that satisfies the holographic principle

Abstract: Conventional wisdom holds that any region of 3-space contains infinitely many points, and the Planck length scale determines the uncertainty in every measurement of distance between two separate points. Against such a backdrop, this uncertainty may be interpreted as resulting from either foaminess or discreteness of 3-space. But, as it is demonstrated in the present paper, neither of those interpretations is consistent with the holographic principle. In the paper it is shown that the statement The holographic principle holds true'' and the statementEach region in 3-space contains only a finite number of points'' are logically equivalent.