  In Alm-Hirsch-Maddux (2016), relation algebras $\mathfrak{L}(q,n)$ were
defined that generalize Roger Lyndon's relation algebras from projective lines,
so that $\mathfrak{L}(q,0)$ is a Lyndon algebra. In that paper, it was shown
that if $q>2304n^2+1$, $\mathfrak{L}(q,n)$ is representable, and if $q<2n$,
$\mathfrak{L}(q,n)$ is not representable. In the present paper, we reduced this
gap by proving that if $q\geq n(\log n)^{1+\varepsilon}$, $\mathfrak{L}(q,n)$
is representable.
