Robustness aspects of nested balanced incomplete block designs against missing data have been investigated using connectedness and efficiency criteria. Sufficient condition for robustness of a design has been obtained for the loss of any m observations, using connectedness criterion. Designs robust against the loss of any m observations belonging to one sub-block, loss of any two observations b...

The purpose of this paper is to present a large number of highly A-efficient incomplete block designs for making comparisons among a set of test treatments and a control treatment. These designs are BTIB designs. A simple method of construction of BTIB designs, based on BIB designs is proposed. The advantage of this method is that one can use the vast literature on BIB designs to obtain a large...

This paper describes a modification of the conventional M-ary Differential Phase Shift Keying MDPSK scheme. This method reduces the number of phases which improves the performance of the system by applying a mathematical method from the combinatorial theory called Balanced Incomplete Block Design BIB-design. It is a coding modulation technique in which the signal is represented by a set of phas...

Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric bal...

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.

Some construction methods of the variance balanced block designs with repeated blocks are given. They are based on the incidence matrices of the balanced incomplete block designs with repeated blocks.