  Following our earlier work \cite{sunandan1, sunandan2}, we derive
noncommuting phase-space structures which are combinations of both the
$\kappa$-Minkowski and Snyder algebra by exploiting the reparametrisation
symmetry of the recently proposed Lagrangian for a point particle \cite{subir}
satisfying the exact Doubly Special Relativity dispersion relation in the
Magueijo-Smolin framework.
