  Uniquely represented data structures represent each logical state with a
unique storage state. We study the problem of maintaining a dynamic set of $n$
keys from a totally ordered universe in this context.
  We introduce a two-layer data structure called
$(\alpha,\varepsilon)$-Randomized Block Search Tree (RBST) that is uniquely
represented and suitable for external memory. Though RBSTs naturally generalize
the well-known binary Treaps, several new ideas are needed to analyze the {\em
expected} search, update, and storage, efficiency in terms of block-reads,
block-writes, and blocks stored. We prove that searches have
$O(\varepsilon^{-1} + \log_\alpha n)$ block-reads, that $(\alpha,
\varepsilon)$-RBSTs have an asymptotic load-factor of at least
$(1-\varepsilon)$ for every $\varepsilon \in (0,1/2]$, and that dynamic updates
perform $O(\varepsilon^{-1} + \log_\alpha(n)/\alpha)$ block-writes, i.e.
$O(1/\varepsilon)$ writes if $\alpha=\Omega(\frac{\log n}{\log \log n} )$. Thus
$(\alpha, \varepsilon)$-RBSTs provide improved search, storage-, and
write-efficiency bounds in regard to the known, uniquely represented B-Treap
[Golovin; ICALP'09].
