In this work, we introduce a natural notion concerning finite vector spaces. A family of k-dimensional subspaces of ${\mathbb{F}}_q^n$, which forms a partial spread, is called almost affinely disjoint if any $(k+1)$-dimensional subspace containing a subspace from the family non-trivially intersects with only a few subspaces from the family. The central question discussed in the paper is the polynomial growth (in q) of the maximal cardinality of these families given the parameters k and n. For the cases $k=1$ and $k=2$, optimal families are constructed. For other settings, we find lower and upper bounds on the polynomial growth. Additionally, some connections with problems in coding theory are shown.

在这项工作中，我们引入了一个关于有限向量空间的自然概念。一族k维子空间${\mathbb{F}}_q^n$，形成部分传播，被称为几乎仿射不相交（如果有的话） $(克+1)$包含来自该族的子空间的 -维子空间与来自该族的仅几个子空间非平凡地相交。论文中讨论的中心问题是给定参数k和n的这些族的最大基数的多项式增长（在q 中）。对于案例$克=1$ 和 $克=2$, 最优族被构建。对于其他设置，我们找到多项式增长的下限和上限。此外，还显示了与编码理论问题的一些联系。