Sample random rows within each group in a data.table

How would you use data.table to efficiently take a sample of rows within each group in a data frame?

DT = data.table(a = sample(1:2), b = sample(1:1000,20))
DT
    a   b
 1: 2 562
 2: 1 183
 3: 2 180
 4: 1 874
 5: 2 533
 6: 1  21
 7: 2  57
 8: 1  20
 9: 2  39
10: 1 948
11: 2 799
12: 1 893
13: 2 993
14: 1  69
15: 2 906
16: 1 347
17: 2 969
18: 1 130
19: 2 118
20: 1 732

I was thinking of something like: DT[ , sample(??, 3), by = a] that would return a sample of three rows for each "a" (the order of the returned rows isn't significant):

    a   b
 1: 2 180
 2: 2  57
 3: 2 799
 4: 1  69
 5: 1 347
 6: 1 732

Maybe something like this?

> DT[,.SD[sample(.N, min(3,.N))],by = a]
   a   b
1: 1 744
2: 1 497
3: 1 167
4: 2 888
5: 2 950
6: 2 343

(Thanks to Josh for the correction, below.)

I believe joran's answer can be further generalized. The details are here (How do you sample groups in a data.table with a caveat) but I believe this solution accounts for cases where there aren't "3" rows to sample from.

The current solution will error out when it tries to sample "x" times from rows that have less than "x" common values. In the below case, x=3. And it takes into consideration this caveat. (Solution done by nrussell)

set.seed(123)
##
DT <- data.table(
  a=c(1,1,1,1:15,1,1), 
  b=sample(1:1000,20))
##
R> DT[,.SD[sample(.N,min(.N,3))],by = a]
     a   b
 1:  1 288
 2:  1 881
 3:  1 409
 4:  2 937
 5:  3  46
 6:  4 525
 7:  5 887
 8:  6 548
 9:  7 453
10:  8 948
11:  9 449
12: 10 670
13: 11 566
14: 12 102
15: 13 993
16: 14 243
17: 15  42