Tight single-change covering designs with v = 12, K = 4

Standardised tight single-change covering designs with upsilon = 12, k = 4 are enumerated and classified. There are 2554 of them, and these fall into 566 sets such that, within any set, the designs can be regarded as minor variants of one another. The sets pair off naturally, to give 283 classes of the designs. If any one design in a class is row-regular (or element-regular), then all the designs in the class are row-regular (or element-regular). Of the 283 classes, just 10 comprise row-regular designs; these 10 include the only one of the 283 classes that comprises element-regular designs. Representative members of the 10 row-regular classes are tabulated. Other properties of the designs are discussed. An indication is given of how each of the 10 representative row-regular designs can readily be converted into a row-regular tight single-change covering design with upsilon = 13, k = 4.