regular graph on $v = 1+4g$ vertices. Observe that $( \sqrt{v}-\sqrt{v+5/4} )/2$ tends to $0$ as $v$ tends to infinity. Using Fejér’s theorem (see Kuipers and Niederreiter [@Kuip:1974uniform page 13]), it is straightforward to show that the sequence $(\sqrt{1+4g}/2)_{g \in \mathbb{N}}$ is uniformly distributed modulo $1$. Therefore we can apply Theorem \[thm:beatDelsarteConf\] to about a quarter of all feasible parameter tuples for type-I strongly regular graphs.

Let $\mathcal P$ denote the set of all primes $p$ of the form $p = 1+4g$ for some $g \in \mathbb N$. Then the sequence $(\sqrt{p}/2)_{p \in \mathcal{P}}$ is uniformly distributed modulo $1$ (see Balog [@Balog:85 Theorem 1]). Therefore, since Paley graphs on $p$ vertices exist for all $p \in \mathcal P$, Theorem \[thm:beatDelsarteConf\] is applicable to infinitely many strongly regular graphs.

Note that the example in [@Soi:CAB15] with parameters $(65,32,15,16)$ is an example of a (potential) graph satisfying the hypothesis of Theorem \[thm:beatDelsarteConf\].

A graph is called **co-connected** if its complement is connected. We have the following:

\[thm:beatDelsarteNonConf\] Let $\Gamma$ be a co-connected type-II strongly regular graph with parameters $(v,k,\lambda,\mu)$ and eigenvalues $k > r \geqslant s$. Suppose that $$0 < {\operatorname{frac} \left ( -k/s \right )} < 1 - (r^2 + r)/(v 