Abstract
Spread sets of projective planes of order q3 are represented as sets of q3 points in A ≅ AG(3, q3). A line through the origin in A can be interpreted as a space A0 ≅ AG(3, q), and the spread set induces a cubic surface L in A0. If the projective plane is a semifield plane of dimension 3 over its kernel, then L has the property that it misses a plane of A0. Determining all such surfaces L leads to a complete classification of the semifield planes of order q3, whose spread sets are division algebras of dimension 3.
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