Eventual existence at all sufficiently large orders

Determine whether there exists an integer n₀ such that a pair of orthogonal quantum Latin squares of order n, each having maximal cardinality n², exists for every n ≥ n₀.

Background

The paper proves existence of MCOQLS(n) for two broad families of orders obtained from finite abelian group factorizations and product constructions. These families do not cover every sufficiently large integer, so it remains unresolved whether the existence property eventually holds for all orders beyond a universal threshold.