Some 6 x 11 Youden squares and double Youden rectangles

5-cyclic Youden squares of size 6x11 are enumerated and classified into 70 species. In a certain standardised form, there are 249 such Youden squares. Of the 61 752 ordered pairs of these, just 1352 can be used to construct 5-cyclic 6 x 11 double Youden rectangles (DYRs); this gives a 'success rate' of 2.2%. The DYRs fall into 175 species, of which 12 exhibit some symmetry. Hitherto, just a single 5-cyclic 6 x 11 DYR has appeared in print. The results are introduced via the analogous results for 4 x 7 Youden squares and DYRs, and provide encouragement in the search for 2p x (4p - 1)DYRs with p > 3; no such DYR with p > 4 has yet been found; the paper is motivated by the need to explore possible ways of finding some.