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Let q  > 2 ⋅ 3 4 t be even. We prove that the only symplectic semifield spread of PG(5,  q t ) , whose associate semifield has center containing F q , is the Desarguesian spread. Equivalently, a commutative semifield of order q 3 t , with middle nucleus containing F q t and center containing F q , is a field. We do that by proving that the only possible F q -linear set of rank 3 t in PG(5,  q t ) disjoint from the secant variety of the Veronese surface is a plane of PG(5,  q t ) .

Symplectic semifield spreads of PG(5, q^t), q even