Girth 5 Graphs from Elliptic Semiplanes

For 3 <= k <= 20 with k not equal 4, 8, 12, all the smallest currently known k-regular graphs of girth 5 have the same orders as the girth 5 graphs obtained by the following construction: take a (not necessarily Desarguesian) elliptic semiplane S of order n - 1 where n = k - r for some r >= 1; the Levi graph Gamma(S) of S is an n-regular graph of girth 6; parallel classes of S induce co-cliques in Gamma(S), some of which are eventually deleted; the remaining co-cliques are amalgamated with suitable r-regular graphs of girth at least 5. For k > 20, this construction yields some new instances underbidding the smallest orders known so far.