Refined methods for the identifiability of tensors

We prove that the general tensor of size 2^n and rank k has a unique decomposition as the sum of decomposable tensors if k ≤ 0.9997*2^n/(n+1) (the constant 1 being the optimal value). Similarly, the general tensor of size 3^n and rank k has a unique decomposition as the sum of decomposable tensors if k ≤ 0.998*3^n/(2n+1), (the constant 1 being the optimal value). Some results of this flavor are obtained for tensors of any size, but the explicit bounds obtained are weaker.