Abstract:
Researchers present two algorithms for constructing Balanced Incomplete Block Designs (BIBD); the first, for determining the BIBDs that qualify to be Lotto Designs (LD) and the second for generating BIBDs from the LD parameters (n, k, p, t). The algorithms are tested using (υ = 6, b = 20, r = 10, k = 3, λ = 4) and (υ = 13, b = 130, r = 30, k = 3, λ = 4) BIBDs. One of the results, the (υ = 4, b = 4, r = 3, k = 3, λ = 2) BIBD which is pair wise balanced is shown to be D-optimal. Also, the (13, 130, 30, 3, 5) BIBD yielded (13, 56, 21, 3, 6), (13, 84, 28, 3, 7), (13, 120, 36, 3, 8) and (13, 165, 45, 3, 9) BIBDs; the first three being less cumbersome and more economical for experimental purposes. In general, a BIBD that qualifies as a LD can be used to generate other BIBDs.

Abstract:
In this letter, we propose a new pulse position modulation (PPM) scheme, called expurgated PPM (EPPM), for application in peak power limited communication systems, such as impulse radio (IR) ultra wide band (UWB) systems and free space optical (FSO) communications. Using the proposed scheme, the constellation size and the bit-rate can be increased significantly in these systems. The symbols are obtained using symmetric balanced incomplete block designs (BIBD), forming a set of pair-wise equidistance symbols. The performance of Q-ary EPPM is better than any Q-ary pulse position-based modulation scheme with the same symbol length. Since the code is cyclic, the receiver for EPPM is simpler compared to multipulse PPM (MPPM).

Abstract:
The paper briefly discusses the balanced incomplete–block design (BIBD’s) and further compares two methods of analyzing them-the classical and vector space analysis of variance (ANOVA) methods. These methods are applied differently to the data arising from the balanced incomplete block designs (BIBD’s). The basic interest is to compare the performance of the two methods of analysis on the available data from National Root Crop Research Institute (N.R.C.R.I) Umudike, Abia State. To achieve this, we shall consider treatment (adjusted), block (adjusted) treatment (not adjusted) in the classical ANOVA method and the vector space ANOVA method. Block is adjusted to know if the experiment is symmetric balanced incomplete block design (SBIBD). The classical ANOVA method was easier to compute and more convenient to handle than the vector ANOVA method. The classical ANOVA method is found to be preferable to the vector space ANOVA method.

Abstract:
Balanced incomplete block designs (BIBDs) have wide applications in engineering, business and sciences. In this paper, for each (v, k, \lambda)-BIBD, we construct a strongly symmetric k-th order v-dimensional tensor. We call such a strongly symmetric tensor the characterization tensor of that BIBD, and the absolute value tensor of the characterization tensor the signless characterization tensor of that BIBD. We study some spectral properties of such characterization tensors and signless characterization tensors. In this way, we provide a new tool to study BIBDs.

Abstract:
This paperdiscusses a comparative analysis on balanced incomplete block designs by using the classical analysis of variance (ANOVA) method. Fortunately, the data collected for the analysis were in two groups of the balanced incomplete-block designs (BIBD’s), that is, symmetric, and unsymmetric (BIBD’s). In this paper, the basic interest is to apply classical ANOVA on the two types of BIBD’s and check whether they are significant and also minimizes error. A secondary data from N.R.C.R.I, Umudike, Abia State was used. To achieve this, we shall consider treatment (adjusted), block (adjusted) treatment (not adjusted) in the classical ANOVA method on the available data. Though, symmetric balanced incomplete block design (SBIBD) and unsymmetric balanced incomplete block design (USBIBD) are significant, it is pertinent to note that the SBIBD classical ANOVA method is found to be preferable to the USBIBD with reference to their variances at different level of significance.

Abstract:
Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs are also obtained.

Abstract:
A $t\text{-}(n,K,\lambda;q)$ design, also called the $q$-analog of a $t$-wise balanced design, is a set ${\mathcal B}$ of subspaces with dimensions contained in $K$ of the $n$-dimensional vector space ${\mathbb F}_q^n$ over the finite field with $q$ elements such that each $t$-subspace of ${\mathbb F}_q^n$ is contained in exactly $\lambda$ elements of ${\mathcal B}$. In this paper we give a construction of an infinite series of nontrivial $t\text{-}(n,K,\lambda;q)$ designs with $|K|=2$ for all dimensions $t\ge 1$ and all prime powers $q$ admitting the standard Borel subgroup as group of automorphisms. Furthermore, replacing $q=1$ gives an ordinary $t$-wise balanced design defined on sets.

Abstract:
The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).

Abstract:
Bose proved the inequality $b\geq v+r-1$ for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note we prove a new lower bound on the number of blocks $b$ that holds for all BIBDs. We further prove that for a significantly large number of BIBDs our bound is tighter than the bounds given by the inequalities of Bose and Kageyama.

Abstract:
Main effect plans orthogonal through the block factor (POTB) have been defined and a few series of them have been constructed in Bagchi (2010). These plans are very closely related to the `mutually orthogonal balanced nested row-column designs' of Morgan and Uddin (1996) and many other combinatorial designs in the literature with different names like `BIBDs for two sets of treatment', `Graeco-Latin designs' and `PERGOLAs'. In fact all of them may be viewed as POTBs satisfying one or more additional conditions, making them `optimal'. However, the PERGOLAs are defined to satisfy an additional property, without which also it is optimal. Interestingly, this additional property is satisfied by all the hitherto known examples of POTBs, even when their definitions do not demand it. In this paper we present direct and recursive constructions of POTBs. In the process we have constructed one design which seems to be the first example of an `optimal' two-factor POTB which is not a PERGOLA (see Theorem \ref {POTB2}).