Uniform critical sets in Latin squares

In this paper, we introduce two new classes of critical sets, \( t \)-uniform and \( T \)-uniform (where \( t \) is a positive integer and \( T \) is a partial Latin square). We identify, up to isomorphism, all \( t \)-uniform critical sets of order \( n \), where \( 2 \leq n \leq 6 \). We show that the completable product of two \( T \)-uniform critical sets is a \( T \)-uniform critical set for certain partial Latin squares \( T \), and then apply this theorem to small examples to generate infinite families of \( T \)-uniform critical sets.