Table 1.

Statistics on the sparsity and density factor of the universal hitting sets generated by random ordering, the DOCKS universal hitting set and the lexicographic ordering

Ordering	$\mathbf{S}\mathbf{P}(U_{k,w})$	$\left|U_{k,w}\right|/{\sigma }^k$	df	$d_{f,\mathbf{S}\mathbf{P}}$
	%	%
random	0.07	51	1.999	1.998
DOCKS	13.3	21	1.737	1.733
lexicographic	0.00	100	2.236	2.000

The computation is done with k = 10, w = 10 on a binary alphabet. The values for the random ordering are averages over 1000 different randomized orderings. d_f is the density factor and $d_{f,\mathbf{S}\mathbf{P}}$ is the density factor estimated given the sparsity of the set by equation 3. The difference between these numbers is due to the imperfect nature of Hypotheses 2.