The biwheel conjecture for braces

Let $b(n)$ denote the minimum number of perfect matchings in a simple brace of order $n$. De~Carvalho, Lucchesi and Murty (SIAM Journal on Discrete Mathematics, 27(2): (2013) 940-958) proved that $b(n)\ge (n-2{)}^2\mathrm{/}8$ and conjectured that $b(n)=(n-2{)}^2\mathrm{/}4$ for all sufficiently large even $n$. We prove this conjecture.