New Semifield Planes of order 81

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Rúa, I. F.
Combarro, E. F.
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Abstract
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A finite semifield is a finite nonassociative ring with identity such that the set of its nonzero elements is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield planes of orders 81 by means of computational methods. These computer-assisted results yield to a complete classification (up to isotopy) of 81-element finite semifields.
Comment: 14 pages. Revised paper (original title: New semifield planes of orders 64 and 81). U. Dempwolff had previously and independently obtained a classification of finite semifields of order 81 (Semifield Planes of Order 81, J. of Geometry (to appear)). So, the current version (unpublished) contains only the results concerning 81 element finite semifields
Keywords
Mathematics - Rings and Algebras, Mathematics - Combinatorics, 17D99, 17-08
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