Abstract
AbstractGroup divisible covering designs (GDCDs) were introduced by Heinrich and Yin as a natural generalization of both covering designs and group divisible designs. They have applications in software testing and universal data compression. The minimum number of blocks in a k‐GDCD of type is a covering number denoted by . When , the values of have been determined completely for all possible pairs . When , Francetić et al. constructed many families of optimal GDCDs, but the determination remained far from complete. In this paper, two specific 4‐IGDDs are constructed, thereby completing the existence problem for 4‐IGDDs of type . Then, additional families of optimal 4‐GDCDs are constructed. Consequently the cases for whose status remains undetermined arise when and , when and , and in several small families for which one of g and u is fixed.
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