  In this paper, we investigate the numerous parameters choices for linear
lattice Boltzmann schemes according to the definition of the isotropic order
given in \cite{ADG11}. This property---written in a general framework including
all of the \ddqq schemes---can be read through a group operation. It implies
some relations on the parameters of the scheme (equilibrium states and
relaxation times) that give rigorous methodology to select them according to
the desired order of isotropy. For acoustic applications in two spaces
dimensions (namely \ddqn and \ddqt schemes) this methodology is used to propose
a full description of the sets of parameters that involve isotropy of order $m$
($m\in\{1,2,3,5\}$ for \ddqn and $m\in\{1,2\}$ for \ddqt). We then propose
numerical illustrations for the \ddqn scheme.
