The original RCs are concerned with the storage/repair-bandwidth tradeoff for the worst possible helper selection. LRCs, on the other hand, are concerned with only data storage (ignoring repair-bandwidth) of the codes when restricting to SHS and exact-repair. Some recent developments [@kamath2014codes; @kamath2013explicit] in LRCs consider using RCs in the construction of the codes therein (as local codes) in an attempt to examine the repair-bandwidth performance of LRCs. This approach, however, is not guaranteed to be optimal in terms of storage/repair-bandwidth tradeoff.

In this work, we present the first exploration of the optimal storage-bandwidth tradeoff for RCs that allow [*dynamic helper selection (DHS)*]{} for arbitrary $(n,k,d)$ values. The closest setting in the existing literature is in [@hollmann2014minimum]. That work finds upper bounds on the file size $\mathcal{M}$ when $\alpha=d\beta$ and $\alpha=\beta$ for functional-repair with DHS. However, [@hollmann2014minimum] considers the case of $k=n-1$ only. Also, it is not clear whether the provided upper bounds for $k=n-1$ are tight or not. A byproduct of the results of this work shows that the upper bounds in [@hollmann2014minimum] are tight in some cases and loose in others, see Corollary \[cor:existing\_loose\] and Propositions \[prop:optimal\_2\] and \[prop:family-plus\_optimal\].

Preview Of The Results {#sec:preview}
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In the following, we 