Constant-factor bounds for R ≤ 4 tensor decomposition

Determine the minimal achievable constant factors, as functions of the finite field size |F| and the rank R, in polynomial-time algorithms for rank-R decomposition of n×n×n tensors over a fixed finite field when R ≤ 4.

Background

The main result establishes an algorithm with runtime O(n^3 + f(|F|, R)n^2) for fixed R ≤ 4. While polynomial-time is guaranteed, the constants—particularly those depending on |F| and R—may be large in practice. Tightening these constants is important for practical efficiency and theoretical understanding of algorithmic performance.