Designs, Codes and Cryptography, 56 No. 2-3 (2010), 163-175.
In this paper, we consider new results on (k,n)-caps with n>2. We provide a lower bound on the size of such caps. Furthermore, we generalize two product constructions for (k,2)-caps to caps with larger n. We give explicit constructions for good caps with small n. In particular, we determine the largest size of a (k,3)-cap in PG(3,5), which turns out to be 44. The results on caps in PG(3,5) provide a solution to four of the eight open instances of the main coding theory problem for q=5 and k=4.
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