  An access structure specifying the qualified sets of a secret sharing scheme
must have information rate less than or equal to one. The Vamos matroid induces
two non-isomorphic access structures V1 and V6, which were shown by Marti-Farre
and Padro to have information rates of at least 3/4. Beimel, Livne, and Padro
showed that the information rates of V1 and V6 are bounded above by 10/11 and
9/10 respectively. Here we improve those upper bounds to 19/21 for V1 and 17/19
for V6.
