Open surfaces of small volume

We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1\mathrm{/}48983$ and a log canonical pair $(X,B)$ with a nonempty reduced divisor $B$ and ample $K_X+B$ that has $(K_X+B{)}^2=1\mathrm{/}462$. Both examples significantly improve known records.