List strong rainbow connection number of wheels

Determine src^ℓ(W_n) for every integer n≥3, where W_n is the wheel graph formed from the cycle C_n by adding a universal vertex.

Background

The paper determines src^ℓ(W_n) exactly for 3≤n≤9 and gives lower and upper bounds for n≥10. It also proves that computing src^ℓ(W_n) for n≥7 is equivalent to computing the list chromatic number of the complement of the square of C_n.

The authors state that they expect the correct value to be substantially smaller than the upper bound of approximately 4n/9, but leave the exact determination unresolved.