consider a matrix with 16 rows and 5000 columns. $ \frac{16!}{8!8!} = 12870 $ amon them select 5000 combinations call them $ \ c_{1},c_{2},....c_{5000} $ then proceed like following for i-th column fill up the places indicated by c_{i} with the element i.and the remaining 8 places in that i-th column by the element 5000+i. then take the row1,row2,...row16. they will be 16 such subsets.