Recent Results

In this section, we intend to record new results as they become known to us. The format of this section will change when the present listing becomes unwieldly.
(4/27/98) In a preprint that has now been circulating for several months (former title, A Sporadic Semifield Flock ... but this has been changed), Bader, Lunardon and Pinneri have constructed a semi-field type flock of a quadratic cone in PG(3, 243) from the translation ovoid of Q(4, 243) found, using a computer, by Penttila and Williams.
This flock is weakly equivalent to [t9, t, t81] in our notation.

(05/13/98) Tim Penttila wrote: "There is a new infinte family of BLT-sets for q congruent to plus or minus 1 modulo 10. For q = 11, you get the DeClerck-Herssens-Thas example. For q = 19 you get the example Gordon [Royle] and I found with a group of order 40. There is a cyclic group of order q + 1 acting regularly on the set, so it only gives one flock. It looks as though the full group will be cyclic q + 1 semidirect cyclic 2h, where q = ph, p prime, for q > 11. The construction is not in the standard model, but rather in (GF(q2),GF(q2),GF(q)) coordinates.