There has been a rapidly increasing demand for developing highly configurable software systems, which urgently calls for effective testing methods. In practice, t-wise coverage has been widely recognized as a useful metric to evaluate the quality of a test suite for testing highly configurable software systems, and achieving high t-wise coverage is important for ensuring test adequacy. However, state-of-the-art methods usually cost a fairly long time to generate large test suites for high pairwise coverage (i.e., 2-wise coverage), which would lead to ineffective and inefficient testing of highly configurable software systems. In this paper, we propose a novel local search based sampling approach dubbed LS-Sampling for achieving high t-wise coverage. Extensive experiments on a large number of public benchmarks, which are collected from real-world, highly configurable software systems, show that LS-Sampling achieves higher 2-wise and 3-wise coverage than the current state of the art. LS-Sampling is effective, since on average it achieves the 2-wise coverage of 99.64% and the 3-wise coverage of 97.87% through generating a small test suite consisting of only 100 test cases (90% smaller than the test suites generated by its state-of-the-art competitors). Furthermore, LS-Sampling is efficient, since it only requires an average execution time of less than one minute to generate a test suite with high 2-wise and 3-wise coverage.