On covering cubic graphs with 3 perfect matchings

For a bridgeless cubic graph G, m₃(G) is the ratio of the maximum number of edges of G covered by the union of $3$ perfect matchings to $|E(G)|$. We prove that for any r∈ [4/5, 1), there exist infinitely many cubic graphs G such that m₃(G) = r. For any r∈ [9/10, 1), there exist infinitely many cyclically $4$-connected cubic graphs G with m₃(G) = r.