Constructing N _γ latin squares for γ ≠ 2 ^α

An Nγ latin square of order n is an n × n latin square containing no latin subsquare of order γ for 1 < γ < n. It has been shown in the literature that if n ≠ 2 ^p3 ^q there exists an n × n latin square without latin subsquare of order γ for γ< n. In this paper, combining with the known results, we show that for any integer n there is an n × n N _γ latin square if γ is not a power of two .