  We derive a stochastic representation for the probability distribution on the
positive orthant $(0,\infty)^d$ whose association between components is minimal
among all probability laws with $\ell_p$-norm symmetric survival functions. It
is given by a transformation of a uniform distribution on the standard unit
simplex that is multiplied with an independent finite mixture of certain beta
distributions and an additional atom at unity. On the one hand, this implies an
efficient simulation algorithm for arbitrary probability laws with
$\ell_p$-norm symmetric survival function. On the other hand, this result is
leveraged to construct an exact simulation algorithm for max-infinitely
divisible probability distributions on the positive orthant whose exponent
measure has $\ell_p$-norm symmetric survival function. Both applications
generalize existing results for the case $p=1$ to the case of arbitrary $p \geq
1$.
