Construction of Neighbor Balanced Block Designs

Abstract

Neighbor designs with complete blocks for all odd v (number of treatments) were generated by Rees (1967). Since then it is a well investigated field. Here, in this study some new algorithms have been developed to generate (a) complete block neighbor designs for v = 4s; s is a natural number, (b) neighbor balanced designs for k = v - 1 when v is odd, (c) neighbor balanced designs for k = v - 1 when v = 4s and (d) all order neighbor balanced complete block designs for v odd prime, in minimum number of blocks when right and left neighbor effects are equal. In all cases blocks are circular and well separated. A catalogue of complete block neighbor designs for v = 4s generated through algorithm given in part (a) is also presented.

Key Words:

• Complete block neighbor designs
• Second order neighbor designs
• All order neighbor balanced designs
• Circular blocks
• Efficient neighbor designs
• Generalized neighbor designs