  We computationally completely enumerate a number of types of row-column
designs up to isotopism, including double, sesqui and triple arrays as known
from the literature, and two newly introduced types that we call mono arrays
and AO-arrays. We calculate autotopism group sizes for the designs we generate.
For larger parameter values, where complete enumeration is not feasible, we
generate examples of some of the designs, and generate exhaustive lists of
admissible parameters. For some admissible parameter sets, we prove
non-existence results. We also give some explicit constructions of sesqui
arrays, mono arrays and AO-arrays, and investigate connections to Youden
rectangles and binary pseud Youden designs.
