Covering Array Tables for t=2,3,4,5,6


These tables are maintained by Charlie Colbourn on an irregular basis. Please report updates and corrections.

For given t and v, the table (t,k,v) gives the current best known upper bound on CAN(t,k,v), the smallest number of rows in a uniform covering array having k factors each with v levels, with coverage at strength t. Covering array numbers are reported for each k up to 20000 for strength two, 10000 for strengths three through six. At present, the authorities are not given with references.

`Best known' means best reported in the literature, to me via email, or implied by a recursive construction. Sizes are reported when an explicit construction is known, not when a probabilistic argument guarantees existence. However, for certain values of v when t is 4, 5, or 6, a constructive conditional expectation algorithm yields better bounds than those implied by the direct and recursive methods -- in these cases, the accompanying graph shows two lines, of which the lower one shows the bounds from the conditional expectation method.

(2,k,2)(2,k,3)(2,k,4)(2,k,5)(2,k,6)(2,k,7)(2,k,8)(2,k,9)(2,k,10)(2,k,11)(2,k,12)(2,k,13)(2,k,14)(2,k,15)(2,k,16)(2,k,17)(2,k,18)(2,k,19)(2,k,20)(2,k,21)(2,k,22)(2,k,23)(2,k,24)(2,k,25)
(3,k,2)(3,k,3)(3,k,4)(3,k,5)(3,k,6)(3,k,7)(3,k,8)(3,k,9)(3,k,10)(3,k,11)(3,k,12)(3,k,13)(3,k,14)(3,k,15)(3,k,16)(3,k,17)(3,k,18)(3,k,19)(3,k,20)(3,k,21)(3,k,22)(3,k,23)(3,k,24)(3,k,25)
(4,k,2)(4,k,3)(4,k,4)(4,k,5)(4,k,6)(4,k,7)(4,k,8)(4,k,9)(4,k,10)(4,k,11)(4,k,12)(4,k,13)(4,k,14)(4,k,15)(4,k,16)(4,k,17)(4,k,18)(4,k,19)(4,k,20)(4,k,21)(4,k,22)(4,k,23)(4,k,24)(4,k,25)
(5,k,2)(5,k,3)(5,k,4)(5,k,5)(5,k,6)(5,k,7)(5,k,8)(5,k,9)(5,k,10)(5,k,11)(5,k,12)(5,k,13)(5,k,14)(5,k,15)(5,k,16)(5,k,17)(5,k,18)(5,k,19)(5,k,20)(5,k,21)(5,k,22)(5,k,23)(5,k,24)(5,k,25)
(6,k,2)(6,k,3)(6,k,4)(6,k,5)(6,k,6)(6,k,7)(6,k,8)(6,k,9)(6,k,10)(6,k,11)(6,k,12)(6,k,13)(6,k,14)(6,k,15)(6,k,16)(6,k,17)(6,k,18)(6,k,19)(6,k,20)(6,k,21)(6,k,22)(6,k,23)(6,k,24)(6,k,25)


If you are interested in explicit presentations of covering arrays, which are not necessarily the best known, a good place to start is at the NIST Covering Array Tables. Some explicit solutions are also available from Jose Torres Jimenez here -- click on Covering Arrays.