From a computational point of view one can probably use the LLL algorithm for getting fairly good solutions: Indeed consider the sublattice of $\mathbb Z^(n+2)$$\mathbb Z^{n+2}$ spanned by integral vectors of the form $(0,\dots,0,1,0,\dots,\lfloor A\cos(2\pi k/n)\rfloor,\lfloor A\sin(2\pi k/n)\rfloor)$. Fine-tuning of the the real number $A$ (which has to be choosen not too small) and searching for a short vector in this lattice yields solutions. Using known bounds for lattice packings yields perhaps some useful upper bounds (but the computations are probably a little tricky).
From a computational point of view one can probably use the LLL algorithm for getting fairly good solutions: Indeed consider the sublattice of $\mathbb Z^(n+2)$ spanned by integral vectors of the form $(0,\dots,0,1,0,\dots,\lfloor A\cos(2\pi k/n)\rfloor,\lfloor A\sin(2\pi k/n)\rfloor)$. Fine-tuning of the the real number $A$ (which has to be choosen not too small) and searching for a short vector in this lattice yields solutions. Using known bounds for lattice packings yields perhaps some useful upper bounds (but the computations are probably a little tricky).
From a computational point of view one can probably use the LLL algorithm for getting fairly good solutions: Indeed consider the sublattice of $\mathbb Z^{n+2}$ spanned by integral vectors of the form $(0,\dots,0,1,0,\dots,\lfloor A\cos(2\pi k/n)\rfloor,\lfloor A\sin(2\pi k/n)\rfloor)$. Fine-tuning of the the real number $A$ (which has to be choosen not too small) and searching for a short vector in this lattice yields solutions. Using known bounds for lattice packings yields perhaps some useful upper bounds (but the computations are probably a little tricky).
From a computational point of view one can probably use the LLL algorithm for getting fairly good solutions: Indeed consider the sublattice of $\mathbb Z^(n+2)$ spanned by integral vectors of the form $(0,\dots,0,1,0,\dots,\lfloor A\cos(2\pi k/n)\rfloor,\lfloor A\sin(2\pi k/n)\rfloor)$. Fine-tuning of the the real number $A$ (which has to be choosen not too small) and searching for a short vector in this lattice yields solutions. Using known bounds for lattice packings yields perhaps some useful upper bounds (but the computations are probably a little tricky).