Mathematics, Department of


Date of this Version

April 1967


Published in The Annals of Mathematical Statistics, Vol. 38, No. 2. (Apr., 1967), pp. 571-581. Copyright © 1967 Institute of Mathematical Statistics. Used by permission. The Annals of Mathematical Statistics is superceded by The Annals of Statistics, online at


An extensive family of two-class PBIB designs is defined in Section 1and given the title of NL designs. Several analogies of NL designs with Latin square type designs are discussed in Sections 1 and 2. Some of these designs have already appeared in scattered contexts. Section 3 gives a construction based on finite geometry for an infinite class of XL designs, and others can be constructed by methods to be taken up elsewhere. An extension to designs with more than two associate classes is indicated in Section 4.

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