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We present two lower bounds on sub-packetization level $\alpha$ of MSR codeswith parameters $(n, k, d=n-1, \alpha)$ where $n$ is the block length, $k$dimension, $d$ number of helper nodes contacted during single node repair and$\alpha$ the sub-packetization level. The first bound we present is for any MSRcode and is given by $\alpha \ge e^{\frac{(k-1)(r-1)}{2r^2}}$.  The second bound we present is for the case of optimal-access MSR codes andthe bound is given by $\alpha \ge \min \{ r^{\frac{n-1}{r}}, r^{k-1} \}$. Thereexist optimal-access MSR constructions that achieve the secondsub-packetization level bound with an equality making this bound tight.  We also prove that for an optimal-access MSR codes to have optimalsub-packetization level under the constraint that the indices of helper symbolsare dependant only on the failed node, it is needed that the support of theparity check matrix is same as the support structure of several other optimalconstructions in literature.

On Lower Bounds on Sub-Packetization Level of MSR codes and On The Structure of Optimal-Access MSR Codes Achieving The Bound