On a refinement of Craig's lattices (Q531350)

Let \(p\) be an odd prime number, \(\zeta\) a primitive \(p\)-th root of unity. The authors construct a family of lattices \(\{{\mathcal T}_p\}\), working in the cyclotomic field \({\mathbb Q}(\zeta)\). For \(p\geq 59\) the center density of the \((p-1)\)-dimensional lattice \(\{{\mathcal T}_p\}\) is at least twice that of the \((p-1)\)-dimensional Craig lattice.