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In computer experiments,designs with a sliced structure are useful for experiments with both qualitative and quantitative factors,and nested designs are preferred when the experiments have multiple levels of accuracy.Space- lling designs with a sliced structure or nested structure have been studied independently.However,it is likely that designs with these two structures are needed simultaneously in some situations,for example,when both the low-accuracy experiment (LE) and high-accuracy experiment (HE) both have quantitative and qualitative factors in a multiple computer experiment.But there are no designs so far to accommodate for such situations.In this paper,based on the permutation method proposed by Qian (2009),we construct a special class of nested Latin hypercube designs (NLHDs) with sliced structures,that is,small sliced Latin hypercube designs (SLHDs) are nested within large SLHDs.In another view,the designs can also be considered as SLHDs with with a nested structure.The construction method is easy to implement and the number of factors is exible.Numerical simulations show the usefulness of the newly proposed designs.