Abstract
The indicator function is an effective tool in studying factorial designs. This paper presents some lower bounds of centered \(L_2\)-discrepancy through indicator function. Some new lower bounds of centered \(L_2\)-discrepancy for \(2^{s-k}\) designs and their complementary designs are given. Numerical results show that our lower bounds are tight and better than the existing results.
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Acknowledgments
The authors greatly appreciate helpful suggestions of the referees and editor-in-chief. This work was partially supported by the National Natural Science Foundation of China (Nos. 11201177, 11271147), China Postdoctoral Science Foundation (No. 2013M531716), Scientific Research Plan Item of Hunan Provincial Department of Education (Nos. 12C0287, 14B146), Jishou University Doctor Science Foundation (No. jsdxxcfxbskyxm201113), Scientific Research Plan Item of Jishou University (No. 13JDY041).
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Ou, Z., Qin, H. & Li, H. Some lower bounds of centered \(L_2\)-discrepancy of \(2^{s-k}\) designs and their complementary designs. Stat Papers 56, 969–979 (2015). https://doi.org/10.1007/s00362-014-0618-2
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DOI: https://doi.org/10.1007/s00362-014-0618-2