Lattices are simplified by removing some of their doubly irreducible elements, resulting in smaller lattices called racks. All vertically indecomposable modular racks of $n \le 40$ elements are listed, and the numbers of all modular lattices of $n \le 40$ elements are obtained by P\'olya counting. SageMath code is provided that allows easy access both to the listed racks, and to the modular lattices that were not listed. More than 3000-fold savings in storage space are demonstrated.

翻译：通过移除部分双不可约元对格进行简化，得到称为"rack"的更小格结构。本文列举了所有$n \le 40$个元素的垂直不可分解模rack，并利用Pólya计数法获得了$n \le 40$个元素的所有模格的数目。提供的SageMath代码可便捷访问所列出的rack以及未列出的模格。论证表明存储空间节省超过3000倍。