On the spectrum of an F-square

Given an F-square of some type F(n; αo, αl, ..., αv-1) what critical set sizes can we obtain for this type? Such a question was considered by Donovan and Howse (1999), in the case of Latin squares. In this note we solve this question for the type F(n;1,n – 1), and also obtain partial results for type F(n; 2,n – 2).