  BMS algebra in three spacetime dimensions can be deformed into a two
parameter family of algebra known as $W(a,b)$ algebra. For $a=0$, we show that
other than $W(0,-1)$, no other $W(0,b)$ algebra admits a non-degenerate
bilinear and thus one can not have a Chern-Simons gauge theory formulation with
them. However, they may appear in a three-dimensional gravity description,
where we also need to have a spin 2 generator, that comes from the $(a=0,b=-1)$
sector. In the present work, we have demonstrated that the asymptotic symmetry
algebra of a spin 3 gravity theory on flat spacetime has both the $W(0,-1)$ and
$W(0,-2)$ algebras as subalgebras. We have also constructed a dual boundary
field theory for this higher spin gravity theory by using the
Chern-Simons/Wess-Zumino-Witten correspondence.
