A new semifield of order 210

In [G. Lunardon, Semifields and linear sets of PG(1,qt)PG(1,qt), Quad. Mat., Dept. Math., Seconda Univ. Napoli, Caserta (in press)], G. Lunardon has exhibited a construction method yielding a theoretical family of semifields of order q2n,n>1q2n,n>1 and nn odd, with left nucleus FqnFqn, middle and right nuclei both Fq2Fq2 and center FqFq. When n=3n=3 this method gives an alternative construction of a family of semifields described in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti, On a generalization of cyclic semifields, J. Algebraic Combin. 26 (2009), 1–34], which generalizes the family of cyclic semifields obtained by Jha and Johnson in [V. Jha, N.L. Johnson, Translation planes of large dimension admitting non-solvable groups, J. Geom. 45 (1992), 87–104]. For n>3n>3, no example of a semifield belonging to this family is known.In this paper we first prove that, when n>3n>3, any semifield belonging to the family introduced in the second work cited above is not isotopic to any semifield of the family constructed in the former. Then we construct, with the aid of a computer, a semifield of order 210 belonging to the family introduced by Lunardon, which turns out to be non-isotopic to any other known semifield.