Construction and investigation of semifield planes of order 256

The authors extend the approach to construct and classify semifield projetive planes using linear space and spread set. They show that 124 semifield (nodesarguesian) planes of rank 2 over the field of order 16, that admit baer involution in linear translation complement, do exist. Non-linear isomorphisms of semifield planes of order 256 are constructed; the order of linear autotopisms’ group is calculated; another confirmation of the well-known hypothesis about the solvability of the group of collineations of semifield planes is obtained.