  Consider an arrangement of $k$ lines intersecting the unit square. There is
some minimum scaling factor so that any placement of a rectangle with aspect
ratio $1 \times p$ with $p\geq 1$ must non-transversely intersect some portion
of the arrangement or unit square. Assuming the lines of the arrangement are
axis-aligned, we show the optimal arrangement depends on the aspect ratio of
the rectangle. In particular, the optimal arrangement is either evenly spaced
parallel lines or an evenly spaced grid of lines. We present the precise aspect
ratios of rectangles for which each of the two nets is optimal.
