In this note we construct a new infinite family of (q - 1)-regular graphs of girth 8 and order 2q(q - 1)(2) for all prime powers q >= 16, which are the smallest known so far whenever q - 1 is not a prime power or a prime power plus one itself.
Abreu, M., Araujo-Pardo, G., Balbuena, C., Labbate, D. A construction of Small (q-1)-Regular Graphs of Girth 8. "Electronic journal of combinatorics", 21 Abril 2015, vol. 22, núm. 2, p. 1-8.