This page is for changes since [AGZ21] was published. As of 9 March 2022, there is only one new existence result: In October 2021 Hadi Kharaghani and Thomas Pender sent the $$CW(341,16^2)$$.
Theorem 6.6 of [AGZ21] uses the $$d=3$$ case of Theorem 6.5. It was an oversight not to note that the same is true for any odd $$d$$, so a stronger theorem is:
Theorem: Let $$q$$ be a prime power. Then a proper $$CW((q^{2e+1}-1)/n,q^{2e})$$ exists for all divisors $$n$$ of $$q-1$$ if $$q$$ is even, and all divisors $$n>1$$ of $$q-1$$ if $$q$$ is odd.