loop quantum gravity
In loop quantum gravity it is assumed that space is not infinitely divisible. The nodes are not space . Actually they are the infinitely divisible part of a matter. The distance between the nodes are not discrete. The distance between the nodes may be 1.5 Planck's length or 2.5 planck's length and so on. So quantization of space is not allowed even in loop quantum gravity. And the the distance between loops are also not multiples of Planck's lenght. My conclusion is that space is infinitely divisible and matter is not.