What is a latent space vector?
The latent vector $z$ is just random noise.

The most frequent distributions for that noise are uniform: $z \sim U[-1,+1]$ or Gaussian: $z \sim \mathcal{N}(0, 1)$ . I am not aware of any theoretical study about the properties derived from different priors, so I think it's a practical choice: choose the one that works best in your case.

The dimensionality of the noise depends on the architecture of the generator, but most of the GANs I've seen use a unidimensional vector of length between 100 and 256. 

In PyTorch, torch.Tensor.random_ and torch.randn can respectively be used to generate uniform and Gaussian noise.