The 177 nearrings of size up to 7 are listed in [29]. Using Sonata, not only some errors in that table have been found ([19]), but it was also extended to all the 68695 nearrings with at most 15 elements. This library is a substantial part of the SONATA package and has been enhanced by 1774 additional nearrings such that it now includes all nearrings with identity up to order 31, except those whose additive groups are elementary abelian of order 16 or 27.