Exact asymptotic constant for Fano subsquares in Latin squares

Determine the exact value of the asymptotic constant governing ζ*(n,S_7)/n^4, where ζ*(n,S_7) is the maximum number of subsquares isotopic to the Fano Latin square S_7 in a Latin square of order n.

Background

The paper proves ζ*(n,S_7)=Θ(n^4), with explicit lower and upper bounds, thereby resolving the order of growth. It does not determine the sharp leading constant and records only bounds on its limsup.