We obtain new linear programming (LP) and constructive bounds for the covering radius of binary orthogonal arrays of strength 2k. Our LP bounds develop in two alternative scenarios. First, if a point \(y \in F_2^n\) , where the covering radius of some orthogonal array \(C \subset F_2^n\) of strength 2k is realized, is such that the farthest point of C to y is not antipodal to y we obtain a bound which is better than the Tietäväinen (or Fazekas-Levenshtein) bound for non-tight arrays (i.e., the cardinality strictly exceeds the Rao lower bound). Second, if all points where the covering radius is realized are such that their antipodes are in C, we obtain a bound which depends on the cardinality of C and is again better whenever the orthogonal array is not tight. We further describe three infinite families of binary orthogonal arrays related to the duals of BCH, Melas, and Zetterberg codes. For these families, we derive lower bounds on the covering radius by applying techniques from algebraic curves over finite fields, while the improved linear programming methods developed in this paper provide upper bounds, leading in some cases to fairly close estimates.
