Classification of small (0, 1) matrices

Denote by An the set of square (0, 1) matrices of order n. The set An, n ⩽ 8, is partitioned into row/column permutation equivalence classes enabling derivation of various facts by simple counting. For example, the number of regular (0, 1) matrices of order 8 is 10160459763342013440. Let Dn, Sn denote the set of absolute determinant values and Smith normal forms of matrices from An. Denote by an the smallest integer not in Dn. The sets D9 and S9 are obtained; especially, a9 = 103. The lower bounds for an, 10 ⩽ n ⩽ 19 (exceeding the known lower bound an ⩾ 2fn − 1, where fn is nth Fibonacci number) are obtained. Row/permutation equivalence classes of An correspond to bipartite graphs with n black and n white vertices, and so the other applications of the classification are possible.