Optimal storage efficiency codes are called minimum-storage regenerating (MSR) and attain one of the two extremal points of the optimal Storage-Bandwidth Tradeoff curve  .
MSR codes require minimum storage space per node, i.e., have . Thus, these codes are Maximum-Distance-Separable (MDS). For this amount of storage, they then minimise the amount of repair-bandwidth as . (See here for the system model and notation.)
When a replacement node is constrained to store the same data as the corresponding failed node, the code is known as an exact-MSR code.
Results on MSR Codes (in chronological order in each subsection)
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