Classification of small (0, 1) matrices

Denote by the set of square (0, 1) matrices of order n. The set , 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 , denote the set of absolute determinant values and Smith normal forms of matrices from . Denote by an the smallest integer not in . The sets and 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 correspond to bipartite graphs with n black and n white vertices, and so the other applications of the classification are possible.