Some large partial ovoids of Q~- (5,q), for odd q

摘要

We give explicit descriptions of some of the largest partial ovoids of Q ~-(5, q) currently known (for q odd). Apart from two generic constructions, the other (sporadic) examples are for fields of order q ≤ 11. As far as we know, most of these results are new. Others were found earlier by computer but have never been described explicitly. All our constructions are formulated using elliptic quadratic forms that are not in standard form.