Solving The Problem Of The Orthogonal Table Quasi-physical Personification Method

Ortheogonal table, which has wide applications in experimental design, codingtheory and computer security is an importan sort of array structres. People usuallyuse the pure mathematical approaches to construct orthogonal tables. This paper weuse the quasi-physical and quasi-sociological methods to solve the problem ofconstructing orthogonal tables.The quasi-physical and quasi-sociological methods for problem-solving is a newapproach to solve problems including NP-completed and other pure mathematicalproblems. As far as the quasi-physical method is concerned, it is a way that peopleactively turn to naturt for wisdom to solving problem. In other words, it works insuch a way that to find natural phenomena which are equivalent to the originalmathematical problem in the physical world and then observe the evolution of themotion of matter in it so as to be inspired to obtain a formalistic algorithm forsolving the mathematical problem. The quasi-sociological method, however, islearning from human beings and their rich social experiences for wisdom to solvingproblem. The quasi-physical method makes the original problem an optimizationproblem in mathematics. There is often the possibility of going to a local minimum of object function when we solve the optimization problem mathematically. As forhow to jump out of the trap of local minimum so that the calculation can head for aregion with better prospects, the quasi-physical method is helpless. However, thequasi-sociological method can give us good strategies for jumping out of a trap oflocal minimum with the help of human beings' behavior and experiences. Supported by 973 national focus program of China on deveIopment of fundamental research, 863 nationaI hightechnoIogy program of Chin4 Chinese science fOundation fOr nationaI doctoral training and project of computerscience open laboraory of the institUte of software of Chinese Academy of Sciences.3 g一 g g abasi叱加ical PP讪 howthe qquasi－ghgsical毗 quasi－sociological methodmo止． SecondlX we uthuther nalsze the nhrsical model on which he quasi－pNsical and quasi－sociological methods for solving S肛 Problembased．Considering a Physical hyPothesis on this model,we construct a counterexaxnple to showthatthe hyPothesis is not eee·Howeve二 itdoes notdamage the goodpractical effectof aPplpinp this phpsical model to solve S盯 problem considering he existence of alsorithlnic region,which reflects that the quasi－sociological method is very necessw for ass呐ng the high efficient of＊theent Whole algori灿m therefore deepens our comprehension on the quasi－physical and quasi－sociological methods． mird1X we Wpl…叫nAs恤ysi阴1md q阻SI－500i呐I0alm毗cd引0咖We mathematical Problem ofcom恤non oforthogonal tMles．M successfully es恤fish a physicalopttrizatbo model for sotring satUrated o汕ogonal tables,whwh ws Provedto be correctintheo0 We thi冰。w goodPersonated s咖egies forjumping out of＊the t呷 oflocal minimum using quasi－sociological method based onthe physical model．Thus wegetthe wholequasi－physicaland quasi－sociological algoriM forthe problem ofconsWction ofs咖Med orthogonal tables．he experimental results showthatthephysical model ishighly efficientthanthe conflMng nlllllber mode！based on me pure m她ematical 讪kgfound．他 sucoes讪11y——rk咖M枷ons讪卿nal邮ie WIth 3 leVe13 using th叫U％1－ physical and quasi－sociological algori恤．We got some o汕ogonal t劝les ofL。,(3'') which are not isomorphic．Moreove乙 some ofour results are also not isomorphic to oe results pearedb山e open rekrences we got lip to now LastlX for让卜 ancie口戊扯d importantproblemsofconstfUtfUction ofLatin...