Exponential-size conjecture for jointly constrained address sets

Prove that the number of length-n DNA address sequences that simultaneously satisfy GC-prefix balance, large mutual Hamming distance, mutual uncorrelatedness, and absence of secondary structure grows exponentially in n.

Background

The paper presents constructions and bounds showing exponential growth for sets satisfying subsets of the constraints (e.g., GC-balance with distance, mutual uncorrelatedness), suggesting that the simultaneous enforcement of all four may still permit exponentially many sequences.

Motivated by these partial results and prior work showing exponentially large families avoiding secondary structure, the authors conjecture exponential growth for the fully constrained case.

References

We conjecture that the number of such sequences is exponential in n, since the number of words that satisfy C1+C2, C3, and C1+C3 separately is exponential (see Theorems \ref{thm:M1},\ref{thm:M2}, \ref{thm:M3}).

— DNA-Based Storage: Trends and Methods  (1507.01611 - Yazdi et al., 2015) in Section “Constrained Coding for Address Sequences” (within Random Access and Rewritable DNA-Based Storage)