this function is used in each step of the Weng optimization and for the initialization of the XiaoXu optimization
an OA (ideally maximin optimized GMA OA)
the number of levels of each column in Dp
ell*s
is the target number of levels of the outgoing Dc
a list of m lists of length s permutations of the elements of the replacement vector
a matrix of the same size as Dp