  For non-negative integers $r\ge d$, how small can a subset $C\subset F_2^r$
be, given that for any $v\in F_2^r$ there is a $d$-flat passing through $v$ and
contained in $C\cup\{v\}$? Equivalently, how large can a subset $B\subset
F_2^r$ be, given that for any $v\in F_2^r$ there is a linear $d$-subspace not
blocked non-trivially by the translate $B+v$? A number of lower and upper
bounds are obtained.
