正交阵列的嵌套问题研究.docx

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11、gonalarraysbelongtoanimportantandhigh-profileareaofcombinatoricsandstatistics.Nestedorthogonalarrayswereintroducedtoconstructnestedspacefillingdesignswhichhavebeenproposedforconductingmultiplecomputerexperimentswithdifferentlevelsofaccuracywheretheexpensiveoneofhigheraccuracytoben

12、estedinalargerandrelativelyinexpensiveoneofloweraccuracy.Nestedorthogonalarraysarecloselyrelatedtoincompleteorthogonalarrayswhichareessentialincombinatorialdesigntheoryandextensivelyusedasingredientsintheconstructionofothertypesofdesigns・Inthisthesis,westudiedtheconstructionandexis

13、tenceofnestedorthogonalarraysbyemployingthecorrespondingtechniquesincombinatorialdesigntheory.Bymodifyingsomeknowncombinatorialconstructionsoforthogonalarrayorincompleteorthogonalarray,weestablishedseveralcombinatorialconstructionsofnestedorthogonalarray:t-balanceddesignconstructi

14、on,Wilson-typeconstruction,Identifi・cationconstruction,ConcatenationconstructionandDifferencematrixconstruction.Asanapplicationoftheestablishedconstructions,thefollowingmainresultsabouttheexistenceofnestedorthogonalarrayareobtained:(1)TheexistencespectrumofNOA((st?rt),t+1,(s,r),t)i

15、scompletelydetermined;(2)TheexistencespectrumofLNOA((4r2,r2)?4,(2r,r),2)isalmostcompletelydetermined;(3)TheexistencespectrumofNOA((2s2,d),4,(s，r)52)iscompletelydetermined;(4)PartoftheexistenceresultofNOA((3s2,2c),4,(s,r),2)isobtained,furthermorethecorrespondingexistenceresultofNO

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