On the Composition of Balanced Incomplete Block Designs
- 1 January 1960
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 12, 177-188
- https://doi.org/10.4153/cjm-1960-015-8
Abstract
The object of this paper is to develop a method of constructing balanced incomplete block designs. It consists in utilizing the existence of two balanced incomplete block designs to obtain another such design by what may be called the method of composition.1. Preliminary results on orthogonal arrays and balanced incomplete block designs. Consider a matrix A = (aij) of k rows and N columns, where each aij represents one of the integers 1, 2, … , s. Consider all t-rowed submatrices of N columns, which can be formed from this array, t ≤ k. Each column of any Crowed submatrix can be regarded as an ordered t-plet.Keywords
This publication has 13 references indexed in Scilit:
- ORTHOGONAL LATIN SQUARESProceedings of the National Academy of Sciences, 1959
- ON THE FALSITY OF EULER'S CONJECTURE ABOUT THE NON-EXISTENCE OF TWO ORTHOGONAL LATIN SQUARES OF ORDER 4t + 2Proceedings of the National Academy of Sciences, 1959
- A Note on Incomplete Block Designs with Row BalanceThe Annals of Mathematical Statistics, 1953
- Orthogonal Arrays of Strength two and threeThe Annals of Mathematical Statistics, 1952
- Orthogonal Arrays of Index UnityThe Annals of Mathematical Statistics, 1952
- Factorial Experiments Derivable from Combinatorial Arrangements of ArraysJournal of the Royal Statistical Society Series B: Statistical Methodology, 1947
- THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTSBiometrika, 1946
- AN EXAMINATION OF THE DIFFERENT POSSIBLE SOLUTIONS OF A PROBLEM IN INCOMPLETE BLOCKSAnnals of Eugenics, 1940
- Euler SquaresAnnals of Mathematics, 1922
- Lehrbuch der Combinatorik. By Dr. Eugen Netto (Pp. 260). 1901. (Teubner.)The Mathematical Gazette, 1902