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A finite semifield is a finite nonassociative ring with identity such thatthe set of its nonzero elements is closed under the product. From any finitesemifield a projective plane can be constructed. In this paper we obtain newsemifield planes of orders 81 by means of computational methods. Thesecomputer-assisted results yield to a complete classification (up to isotopy) of81-element finite semifields.

New Semifield Planes of order 81