To verify that our optimal set does have low misbinding, we took the largest optimized ensemble of 8 nt sequences we found, containing 48 sequences, and analyzed ΔG of all the possible interactions (Figure ). Figure reveals a nearly ideal energy distribution for self-assembly, with the native interaction ε being generally well-separated in energy from both non-specific interactions ε' and ε''. Importantly, all sequences within this ensemble satisfy ε'/ε < (ε'/ε)c = 0.6 as desired (Figure ). However, since the sequence design scheme ignores the potentially high misbinding that could result after the formation of the dangling end, a small fraction of sequences can exhibit ε'/ε > (ε'/ε)c (Figure ). This would still allow for reliable self-assembly if these problematic sequences were removed. Nevertheless, our design scheme is able to create an ensemble of sequences with much smaller misbinding values (mean of ε'/ε = 0.21 in Figure ) than ensembles that are randomly generated (mean of ε'/ε = 0.61 in Figure ), an approach commonly used in experiments. Thus our rational design procedure is expected to greatly improve the chance of successful programmable self-assembly of various structures using DNA (collection of sequences used in Figures and is provided in Supporting Information, Section S6). a Since the development of square tiles is prone to steric hindrance (Figure ), these optimal sequence ensembles may not be able to guarantee assembly of multiple copies of square tiles. However, such limits could still improve the yield, as one factor that frustrates successful self-assembly, misbinding, is mitigated. Moreover, we can estimate the limits of the size of target structures that can be successfully assembled (Table ). For reference, a chain containing N blocks requires 2(N-1) unique sequences (N-1 sequences and N-1 reverse complements) and a square tile of size N × N blocks requires 4N(N-1) unique sequences. Interestingly, this sequence design scheme and analysis suggest that having longer sequences does not immediately entail their larger number, viz. blocks, that can be used for self-assembly. For example, after application of our established rules, we find that the number of sequences in the 6 nt ensembles, which can contain anywhere from 0 to 8 unique sequences (0 means that ε'/ε < (ε'/ε)c = 0.6 was not possible), is comparable to that of the 7 nt ensembles, which can contain 0 to 12 sequences. Consequently, the sequences in some 7 nt ensembles may not be able to create chains as large as those in some 6 nt ensembles. However, longer sequences can still generally increase the number of optimal sequences within the curated ensemble and accordingly the maximum size of the target structure: we found that an ensemble of 8 nt can contain a maximum of 48 optimal sequences after sequence optimization, which could create a 4 × 4 tile that is larger than the 2 × 2 tile possible using a 6 or 7nt sequence. We note that the maximum structure sizes denoted here are highly conservative since they were based on utilizing the most stringent thermodynamic parameters that would allow for reliable and complete addressability with perfect yield, i.e., ɑ = 1. Larger structures could be synthesized by application of the rules with larger (ε'/ε)c, but at the expense of yield.