Symplectic 4-dimensional semifields of order 84 and 94

We classify symplectic 4-dimensional semifields over F-q, for q <= 9, thereby extending (and confirming) the previously obtained classifications for q <= 7. The classification is obtained by classifying all symplectic semifield subspaces in PG(9, q) for q < 9 up to K-equivalence, where K <= PGL(10, q) is the lift of PGL(4, q) under the Veronese embedding of PG(3, q) in PG(9, q) of degree two. Our results imply the non-existence of non-associative symplectic 4-dimensional semifields for q even, q <= 8. For q odd, and q <= 9, our results imply that the isotopism class of a symplectic non-associative 4-dimensional semifield over F(q )is contained in the Knuth orbit of a Dickson commutative semifield.