Hollmann's pseudocyclicity conjecture for the Frobenius fusion scheme

Let $q=2^m$, let ${\cal E}$ be the set of exterior lines to a fixed nonsingular conic in ${\rm PG}(2,q)$, and let $({\cal E},\{\Gamma_a\})$ be the elliptic association scheme. For $a\in {\bf T}_0^*$, define the Frobenius orbit

$$C_a=\{a,a^2,a^4,\ldots,a^{2^{m-1}}\}$$

and set

$$\Delta_a=\bigcup_{i\in C_a}\Gamma_i.$$

Let ${\cal R}$ be a set of representatives for the Frobenius orbits on ${\bf T}_0^*$. The fusion scheme $({\cal E},\{\Delta_a\})$ is obtained by merging the classes of the elliptic scheme along these orbits.

Hollmann's conjecture. If $m$ is an odd prime, then $({\cal E},\{\Delta_a\})$ is pseudocyclic.

When $m$ is prime, each nontrivial Frobenius orbit has size $m$, so the fusion scheme has equal nontrivial valencies. The conjecture asserts the remaining condition needed for pseudocyclicity; the source gives no resolution.