  This work shows that the smallest natural number $d_n$ that is not the
determinant of some $n\times n$ binary matrix is at least $c\,2^n/n$ for
$c=1/201$. That same quantity naturally lower bounds the number of distinct
integers $D_n$ which can be written as the determinant of some $n\times n$
binary matrix. This asymptotically improves the previous result of
$d_n=\Omega(1.618^n)$ and slightly improves the previous result of $D_n\ge
2^n/g(n)$ for a particular $g(n)=\omega(n^2)$ function.
