Lower bound on a vanilla put from digital puts

You want to value a European put with strike $15$. Digital puts paying $1$ if $S_T\le K$ are available at these prices: $K=15$ at $0.83$, $K=12.5$ at $0.64$, $K=10$ at $0.42$, $K=7.5$ at $0.31$, $K=5$ at $0.20$. Using a portfolio of these digitals whose payoff never exceeds the put's, what is the highest price you can guarantee for the put (the best sub-replication bound)?

$3.925$. Holding $2.5$ digital puts at each strike $12.5,10,7.5,5$ gives a staircase lying under $(15-S_T)^+$ and touching it at each strike. Its cost is $2.5(0.64+0.42+0.31+0.20)=3.925$ (using the $15$ strike as well would give the matching upper bound $5.5$).