p-1阶均匀设计

HOMOGENEOUS DESIGNS OF ORDER p-1

方开泰在研究均匀设计时,对于q=p-1,p为素数的情形,推荐采用布点 P_q(k)=(k,ka,ka^2,…,ka^(s-1))(mod p),k=1,2,…,q,(1.1)其中0<α<p,α的次数≥s(见[1],布点原则(2.3));并且指出:经验证明,对相当多的q=p-1,用上述布点造出的表比用q本身的缩系造的表,不仅列多而且点布得更均匀. 本文旨在证明:对于任意奇素数p,如果把(1.1)式中的α取成模p的任一原根。

A quantitative approach to the homogeneity of the point-setting principle for case q =p - 1 as suggested by Fang Kaitai is presented. And then, a lower bound of the maximumof smallest row distances of cyclic Latin squares of order P - 1 is obtained.