A biplane is a symmetric 2 − (v, k,2) design. Until now, seventeen biplanes with seven different triple of parameters are known. Out of which, biplanes with 56 and 79 points are not classified but only a few individual examples are known. Biplanes are highly regular structures, the space solution size of which extremely increases with number of points (combinatorial explosion). Additional difficulty in construction of this structure is a very small number of structures (results) in space solution. Biplanes of order 2, 3, 4 and 7 are classified by deterministic algorithm (exhaustive search). By searching using additional presumptive condition (each element on the main diagonal of incidence matrix is 1) two biplanes 2 − (56,11,2) are constructed. By searching using the same condition in the case of 2 − (37,9,2) it is observed that a number of incidence matrix is unambiguously determined by number of appropriate vectors of (k + 2) nd row. An analogous regularity appears on testing sample 2 − (56,11,2) . Experiments with heuristic algorithms showed that construction according to Hussain graphs has smaller space solution than construction with incidence matrix, on certain assumptions. Mathematical simplification of problem, using additional condition on structure and vector filtering had the main impact on achievement.