Lower bounds for constant weight codes

Let
A(n,2\delta,w)
denote the maximum number of codewords in any binary code of length
n
, constant weight
w
, and Hamming distance
2\delta
Several lower bounds for
A(n,2\delta,w)
are given. For
w
and
\delta
fixed,
A(n,2\delta,w) \geq n^{W-\delta+l}/w!
and
A(n,4,w)\sim n^{w-l}/w!
as
n \rightarrow \infty
. In most cases these are better than the "Gilbert bound." Revised tables of
A(n,2 \delta,w)
are given in the range
n \leq 24
and
\delta \leq 5
.