On the number of Steiner triple systems S(2m−1,3,2)S(2m−1,3,2) of rank 2m−m+22m−m+2 over F2F2

We obtain the number of different Steiner triple systems S(2m−1,3,2)S(2m−1,3,2) of rank 2m−m+22m−m+2 over the field F2F2.