Exponential growth conjecture for address sequences satisfying constraints C1–C4

Prove or disprove that the number of DNA address sequences of length n that simultaneously satisfy GC-balanced prefixes (C1), large mutual Hamming distance (C2), mutual uncorrelatedness (C3), and absence of secondary structures (C4) grows exponentially with n.

Background

Designing address sequences that enable selective access while avoiding error-prone patterns requires meeting multiple constraints simultaneously. Analytical counting under all constraints is difficult, so the authors combine combinatorial constructions (balanced error-correcting codes) with expurgation and computational folding checks to produce practical sets.

Based on known exponential counts under individual constraints, the authors conjecture that the joint constrained family also grows exponentially with length n, which would imply scalability of the addressing scheme and minimal rate loss in large systems.