We describe the computer-aided classification of equitable partitions of the $12$-cube with quotient matrix $[[2,10],[6,6]]$, or, equivalently, simple orthogonal arrays OA$(1536,12,2,7)$, or order-$7$ correlation-immune Boolean functions in $12$ variables with $1536$ ones (which completes the classification of unbalanced order-$7$ correlation-immune Boolean functions in $12$ variables). We find that there are $103$ equivalence classes of the considered objects, and there are only two almost-OA$(1536,12,2,8)$ among them. Additionally, we find that there are $40$ equivalence classes of pairs of disjoint simple OA$(1536,12,2,7)$ (equivalently, equitable partitions of the $12$-cube with quotient matrix $[[2,6,4], [6,2,4], [6,6,0]]$) and discuss the existence of a non-simple OA$(1536,12,2,7)$. Keywords: orthogonal arrays, correlation-immune Boolean functions, equitable partitions, perfect colorings, intriguing sets.

翻译：我们描述了具有商矩阵[[2,10],[6,6]]的12-立方体均衡划分的计算机辅助分类，这等价于简单正交阵列OA(1536,12,2,7)，或含1536个1的12变量7阶相关免疫布尔函数（这完成了12变量非平衡7阶相关免疫布尔函数的分类）。我们发现所研究对象共有103个等价类，其中仅存在两个几乎OA(1536,12,2,8)。此外，我们找到了40个不相交简单OA(1536,12,2,7)对的等价类（等价于具有商矩阵[[2,6,4],[6,2,4],[6,6,0]]的12-立方体均衡划分），并讨论了非简单OA(1536,12,2,7)的存在性。关键词：正交阵列，相关免疫布尔函数，均衡划分，完美着色，引人集。