Twisted tensor product group embeddings and complete partial ovoids on quadrics in PG(2t−1,q)

We study the geometry of the groups SL(2,qt) and Sp(2m,qt), m,t 2, q even, in their twisted tensor product representation. We construct families of complete partial ovoids of hyperbolic quadrics in PG(2t−1,q), all attaining the Blokhuis–Moorhouse bound. We identify the stabilizers of the complete partial ovoids.