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

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.