Semifield planes of odd order that admit the autotopism subgroup isomorphic to $A_4$

We evolve an approach to construction and classification of semifield projective planes with the use of the linear space and spread set. We construct the spread set matrix representation for any semifield plane of odd order that admits the Baer involution in translation complement or autotopism subgroup isomorphic to $A_4$. We give the examples of semifield planes of order 81 with the indicated condition.