ABSTRACT
It is fairly well known that there are connections to the theories of flocks of hyperbolic quadrics in PG(3, q) and translation planes with spreads in PG(3, q). In particular, a spread in PG(3, q) that is a union of reguli sharing two common lines produces a flock of a hyperbolic quadric and conversely. Using a blend of these theories, a complete characterization of hyperbolic flocks is given by the beautiful theorem of Thas [1178] and Bader-Lunardon [49]. The flocks corresponding to the regular nearfield planes were constructed by J.A. Thas by geometric methods. That there are flocks corresponding to certain irregular nearfields was independently determined by Bader [38], Baker and Ebert [67] for p = 11 and 23, and Johnson [718].
