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An access structure specifying the qualified sets of a secret sharing schememust have information rate less than or equal to one. The Vamos matroid inducestwo non-isomorphic access structures V1 and V6, which were shown by Marti-Farreand Padro to have information rates of at least 3/4. Beimel, Livne, and Padroshowed that the information rates of V1 and V6 are bounded above by 10/11 and9/10 respectively. Here we improve those upper bounds to 19/21 for V1 and 17/19for V6.

Improved Upper Bounds for the Information Rates of the Secret Sharing Schemes Induced by the Vamos Matroid