Errata: New Constructions for Coverings Designs

A few of the upper bounds given in our 1996 JCD paper seem to have come from a bug in one of our programs. We weren’t able to construct the coverings corresponding to these two entries:

• $C(14,7,3) = 14$
• $C(30,15,4) = 30$

In fact Stanislaw Radziszowski has since shown that C(14,7,3) = 15, so that entry was definitely wrong. Furthermore, other table entries were derived from the two above. Here is the current status of all entries whose upper bound in the paper is unsubstantiated (these bounds are all 1 more than those given in the paper):

• $C(14,7,3) = 15$
• $C(27,14,3) \leq 15$
• $C(28,14,3) \leq 15$
• $C(29,15,3) \leq 15$
• $C(28,15,4) \leq 31$
• $C(29,15,4) \leq 31$
• $C(30,15,4) \leq 31$
• $C(23,16,5) \leq 20$
• $C(27,16,5) \leq 51$

Finally, the publisher mistakenly added two optimality stars to the page proofs: Neither the $(11,7,6)$ covering of size $84$ nor the $(14,5,3)$ covering of size $47$ is known to be optimal; the latter covering has actually been improved upon.