This thesis investigates fast methods for finding short lattice vectors in small dimensions (n < 40), with the goal of designing a practical short-vector utility for lattice reduction algorithms such as LLL or BKZ. The focus is not on computing the exact shortest vector, but on efficiently finding sufficiently short vectors under a fixed computational budget.

Pruned enumeration will serve as the core search engine. The thesis will study how structural information derived from the Gram matrix and Gram–Schmidt orthogonalization can be used to improve enumeration performance by modifying vector ordering, coefficient domains, and search strategies.

The following strategies will be examined:
- baseline pruned enumeration and analysis of ordering effects
- greedy ordering based on Gram–Schmidt diagonal values
- template-based preprocessing that identifies promising subsets of vectors using normalized Gram features
- neural-network predictor trained to rank candidate subsets using Gram/GSO-derived features (optional extension of previous approach, only if time permits)
- restricted-coefficient heuristic search strategies guided by the Gram matrix
- meet-in-the-middle variant applied to selected blocks based on the nearest-neighbor algorithm (optional, depending on the algorithm examined in another thesis).

All approaches will be experimentally evaluated on two lattice families with respect to runtime, enumeration cost, and achieved vector quality. The created code will be publicly available in the IS under the MIT
license.