For N≥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.Comment: Minor revisions and corrections. Published in Journal of
Computational Science, Volume 64, 2022, 101853, ISSN 1877-7503,
https://doi.org/10.1016/j.jocs.2022.10185