Cubic universality conjecture for quasi-complementary sequence sets

Let a quasi-complementary sequence set (QCSS) have set size $M$, flock size $K$, sequence length $N$, and tightness factor $\rho$. It is asymptotically near-optimal when its correlation parameter has the near-optimal asymptotic behavior considered in the paper. Cubic universality conjecture. Every asymptotically near-optimal QCSS with

$$1<\rho\leq 2$$

satisfies

$$M\leq (1+o(1))K^3N^2.$$

The cubic upper bound is proved in the restricted range $\rho<\frac{1+\sqrt{5}}{2}$, and explicit constructions attain $M=K^3N^2+2K^2N+K$, making the cubic exponent asymptotically sharp there. Extending the upper bound to the full near-optimal range $1<\rho\leq 2$ remains open.