  We prove that for a system of indeterminates (X_a) indiced by the P^2(2), the
projective plane over F_2, there exists a 3-3 correspondance compatible with
the incidence structures of P^2(2), such that (X_a) is one of the orbits of it.
  We give two applications of this construction :
  1) for any sufficientely general polynomial P in k[X] over a field k of car.
0, such that its Galois group is a subgroup of L3(2) ((=L2(7)), there exists Q
in k[X] such that the Galois group of P-TQ over k(T) is L3(2). This implies in
particular the so-called "arithmetical lifting property" for L3(2) over k.
  2) There exists a generic polynomial in 7 parameters for polynomials of
degree 7 with Galois group L3(2). This is equivalent to the fact that the
Noether's problem for L3(2) acting over the seven points of P^2(2) has a
positive answer.
