We characterize mixed-level orthogonal arrays in terms of algebraic designs in a special multigraph. We prove a mixed-level analog of the Bierbrauer-Friedman (BF) bound for pure-level orthogonal arrays and show that arrays attaining it are radius-1 completely regular codes (equivalently, intriguing sets, equitable 2-partitions, perfect 2-colorings) in the corresponding multigraph. For the case when the numbers of levels are powers of the same prime number, we characterize, in terms of multispreads, additive mixed-level orthogonal arrays attaining the BF bound. For pure-level orthogonal arrays, we consider versions of the BF bound obtained by replacing the Hamming graph by its polynomial generalization and show that in some cases this gives a new bound. Keywords: orthogonal array, algebraic t-design, completely regular code, equitable partition, intriguing set, Hamming graph, Bierbrauer-Friedman bound, additive codes.

翻译：我们通过特殊多重图中的代数设计来刻画混合水平正交阵列。针对纯水平正交阵列，我们证明了混合水平版本的Bierbrauer-Friedman（BF）界，并证明达到该界的阵列在对应多重图中是半径为1的完全正则码（等价于有趣集、均衡2-划分、完美2-着色）。当水平数为相同素数的幂时，我们通过多重扩散集刻画了达到BF界的加法混合水平正交阵列。对于纯水平正交阵列，我们考虑用多项式推广的Hamming图替换原图得到的BF界变体，并证明在某些情况下这会产生新的界。关键词：正交阵列，代数t-设计，完全正则码，均衡划分，有趣集，Hamming图，Bierbrauer-Friedman界，加法码。