  The sequence reconstruction problem, introduced by Levenshtein in 2001,
considers a communication scenario where the sender transmits a codeword from
some codebook and the receiver obtains multiple noisy reads of the codeword.
Motivated by modern storage devices, we introduced a variant of the problem
where the number of noisy reads $N$ is fixed (Kiah et al. 2020). Of
significance, for the single-deletion channel, using $\log_2\log_2 n +O(1)$
redundant bits, we designed a reconstruction code of length $n$ that
reconstructs codewords from two distinct noisy reads.
  In this work, we show that $\log_2\log_2 n -O(1)$ redundant bits are
necessary for such reconstruction codes, thereby, demonstrating the optimality
of our previous construction. Furthermore, we show that these reconstruction
codes can be used in $t$-deletion channels (with $t\ge 2$) to uniquely
reconstruct codewords from $n^{t-1}+O\left(n^{t-2}\right)$ distinct noisy
reads.
