  We study an approximate version of $q$-query LDCs (Locally Decodable Codes)
over the real numbers and prove lower bounds on the encoding length of such
codes. A $q$-query $(\alpha,\delta)$-approximate LDC is a set $V$ of $n$ points
in $\mathbb{R}^d$ so that, for each $i \in [d]$ there are $\Omega(\delta n)$
disjoint $q$-tuples $(\vec{u}_1,\ldots,\vec{u}_q) $ in $V$ so that
$\text{span}(\vec{u}_1,\ldots,\vec{u}_q)$ contains a unit vector whose $i$'th
coordinate is at least $\alpha$. We prove exponential lower bounds of the form
$n \geq 2^{\Omega(\alpha \delta \sqrt{d})}$ for the case $q=2$ and, in some
cases, stronger bounds (exponential in $d$).
