  It is known that Tardos's collusion-secure probabilistic fingerprinting code
(Tardos code; STOC'03) has length of theoretically minimal order with respect
to the number of colluding users. However, Tardos code uses certain continuous
probability distribution in codeword generation, which creates some problems
for practical use, in particular, it requires large extra memory. A solution
proposed so far is to use some finite probability distributions instead. In
this paper, we determine the optimal finite distribution in order to decrease
extra memory amount. By our result, the extra memory is reduced to 1/32 of the
original, or even becomes needless, in some practical setting. Moreover, the
code length is also reduced, e.g. to about 20.6% of Tardos code asymptotically.
Finally, we address some other practical issues such as approximation errors
which are inevitable in any real implementation.
