Regular Packings of PG (3,q)

Two regular packings of PG(3,q) are constructed wheneverq ≡ 2(mod 3), with each packing admitting a cyclic group of orderq2 + q + 1 acting regularly on the regular spreads in the packing. The resulting families of translation planes of orderq4include the Lorimer–Rahilly and Johnson–Walker planes of order 16.