I guess that's as good as it gets from Math::Combinatorics - doable, but not very natural.

There are plenty of other iterators out there that give all the subsets, though - List::PowerSet, Data::PowerSet, Algorithm::ChooseSubsets - We just have to convert them to give a bit mask instead - ie:

use List::PowerSet qw/powerset_lazy/;
my @set = (0) x $N;
my @C   = (1) x 2**$N;
my $M = 0;
my $ps_itr = powerset_lazy(0 .. $N-1);
while (my $ref_set = $ps_itr->()) {
    $_ = 1 for local @set[@$ref_set];
    $C[ $M ] *= $arr->[ $_ ][ $set[$_] ] for 0 .. $N-1;
    $M++;
}
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