We prove lower bounds on the redundancy necessary to
represent a set $S$ of objects using a number of bits
close to the information-theoretic minimum $\log_2 |S|$,
while answering various queries by probing few bits. Our
main results are:

\begin{itemize}
\item To represent $n$ ternary values $t \in
\zot^n$ in ... more >>>

We prove that to store n bits x so that each
prefix-sum query Sum(i) := sum_{k < i} x_k can be answered
by non-adaptively probing q cells of log n bits, one needs
memory > n + n/log^{O(q)} n.

Our bound matches a recent upper bound of n +
n/log^{Omega(q)} ... more >>>