LetA(n,2\delta,w)denote the maximum number of codewords in any binary code of lengthn, constant weightw, and Hamming distance2\deltaSeveral lower bounds forA(n,2\delta,w)are given. Forwand\deltafixed,A(n,2\delta,w) \geq n^{W-\delta+l}/w!andA(n,4,w)\sim n^{w-l}/w!asn \rightarrow \infty. In most cases these are better than the "Gilbert bound." Revised tables ofA(n,2 \delta,w)are given in the rangen \leq 24and\delta \leq 5.