  For $N \geq 2$, an $N$-qubit doily is a doily living in the $N$-qubit
symplectic polar space. These doilies are related to operator-based proofs of
quantum contextuality. Following and extending the strategy of Saniga et al.
(Mathematics 9 (2021) 2272) that focused exclusively on three-qubit doilies, we
first bring forth several formulas giving the number of both linear and
quadratic doilies for any $N > 2$. Then we present an effective algorithm for
the generation of all $N$-qubit doilies. Using this algorithm for $N=4$ and
$N=5$, we provide a classification of $N$-qubit doilies in terms of types of
observables they feature and number of negative lines they are endowed with. We
also list several distinguished findings about $N$-qubit doilies that are
absent in the three-qubit case, point out a couple of specific features
exhibited by linear doilies and outline some prospective extensions of our
approach.
