  Given a prime number l greater than or equal to 5, we construct an infinite
family of three-dimensional abelian varieties over Q such that, for any A/Q in
the family, the Galois representation \rho_{A, l}: Gal_Q -> GSp(6, l) attached
to the l-torsion of A is surjective. Any such variety A will be the Jacobian of
a genus 3 curve over Q whose respective reductions at two auxiliary primes we
prescribe to provide us with generators of Sp(6, l).
