The Ubiquity of the Orders of Fractional Semifields of Even Characteristic

To each non-square integer (2^{2N+1}ge 2^5) there correspond semifields (D) of order of (2^{2N+1}) that contain (text{ GF}(4)) . Hence there exist affine planes for each non-square order (2^{2N+1}ge 2^{5}) that contain subaffine planes of order (2^2) . Moreover, there also exists semifields (D_1) and (D_2) , with (|D_1|= |D_2| =|D|) such that (D_1) is commutative and (D_2) is non-commutative but neither (D_1) nor (D_2) contains (text{ GF}(4)) .