區(qū)組長為4組長為3的α-可分解可分組設(shè)計.pdf

1、aResolvableGroupDivisibleDesignswithBlockSizeFourAbstractaResolvableGroupDivisibleDesignswithBlockSizeFourandGroupSizeThreeAbstractAgroupdivisibledesignGD(k，A，￡；饑)isaresolvableifitsblockscanbeparti—tionedintoclassessucht

2、hateachpointofthedesignoccursinpreciselyablocksineachclassThenecessaryconditionsfortheexistenceofsuchadesignareAt(n一1、=r體一1)，bk=rtn，露l耐他andQlraresolvablegroupdivisibledesignshavebeenstudiedbymanyresearchersandfoundtohave

3、anumberofapplicationsForaresolvableGD(3，A，t；tn)，itsexistencehasbeensolvedbYJungnickel，MullinandVanstone【DJungnickel，RCMuUinandSAVanstone，Thespectrumofaresolvableblockdesignswithblocksize3，DiscreteMath97(1991)，269277】andZ

4、hangandDu【YZhangandBDu，aresolvablegroupdivisibledesignswithblocksizethree，JCombinDesigns，13(2005)，1391511ForaresolvableGD(4，九島tn)，whent=1，itisanaresolvable(n，4，A)一BIBD，whoseexistencehasbeensolvedbyFurinoandMullinIsFurino

5、andRCMullin，BlockdesignsandlargeholesandaresolvableBIBDs，JCombinDesigns，l(1903)，101—112】andVasiga，F(xiàn)urinoandLingITMJVasiga，SFurinoandACHLing，Thespectrumofaresolvabledesignswithblocksizefour，JCombinDesigns，9(2001)，1l6】；whe

6、n口=1andA=1，itisaresolvableGD(4，1，t；tn)，whoseexistencehasbeenalmostcompletelysolvedItisshowninthispaperthattheseconditionsarealsosufficientwhen后=4andt=3，exceptforn=4anda=A=1Keywords：groupdivisibledesign；aresolvablegroupdi