A Computer Search for a Projective Plane of Order 12

It was proved in 1989 by a computer search that there does not exist any projective plane of order 10 by Lam, C.W.H., Thiel, L. and Swiercz, S. Whether there is any projective plane of order 12 is still open. The author introduces the ordered matrix of a (v, k, λ) symmetric design, which preserves some row inner product property, and gives some new necessary condition for the existence of the symmetric (v, k, λ) design. As an application we maybe determine whether there is any projective plane of order 12.