HMMT 2016 U35

(Maximal Determinant) In a $17 \times 17$ matrix $M$, all entries are $\pm 1$. The maximum possible value of $|\operatorname{det} M|$ is $N$. Estimate $N$. An estimate of $E>0$ earns $\left\lfloor 20 \min (N / E, E / N)^{2}\right\rfloor$ points.