  We present a finite blocklength performance bound for a DNA storage channel
with insertions, deletions, and substitutions. The considered bound -- the
dependency testing (DT) bound, introduced by Polyanskiy et al. in 2010 --
provides an upper bound on the achievable frame error probability and can be
used to benchmark coding schemes in the practical short-to-medium blocklength
regime. In particular, we consider a concatenated coding scheme where an inner
synchronization code deals with insertions and deletions and the outer code
corrects remaining (mostly substitution) errors. The bound depends on the inner
synchronization code. Thus, it allows to guide its choice. We then consider
low-density parity-check codes for the outer code, which we optimize based on
extrinsic information transfer charts. Our optimized coding schemes achieve a
normalized rate of $88\%$ to $96\%$ with respect to the DT bound for code
lengths up to $2000$ DNA symbols for a frame error probability of $10^{-3}$ and
code rate 1/2.
