摘要
In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis （SMB for short）, we show that any of its minimal elements is a general greedy-reduced basis, and its least element （if exists） is an SMB. Furthermore, we prove the existence of SMB for lattices of dimension up to 6.
In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis （SMB for short）, we show that any of its minimal elements is a general greedy-reduced basis, and its least element （if exists） is an SMB. Furthermore, we prove the existence of SMB for lattices of dimension up to 6.
