  We consider the matroid prophet inequality problem. This problem has been
extensively studied in the case of adaptive mechanisms. In particular, there is
a tight $2$-competitive mechanism for all matroids.
  However, it is not known what classes of matroids admit non-adaptive
mechanisms with constant guarantee. Recently, it was shown that there are
constant-competitive non-adaptive mechanisms for graphic matroids. In this
work, we show that various known classes of matroids admit constant-competitive
non-adaptive mechanisms.
