Some of the upper bounds given by T. Verhoeff (1987) are improved by proving the nonexistence of codes with certain parameters. Necessary preliminary results are stated. The results give rise to upper bounds on d(n, k) for many further values of (n, k) by using simple standard techniques. The further bounds would automatically follow from theorems by using Verhoeff's computerized updating program, but the authors state them here because several of them are required in the proofs of subsequent theorems.>