Let \(q\) be a prime power and \(V\cong\mathbb{F}_q^d\). A \(t\)-\((d,k,\lambda)_q\) design, or simply subspace is pair \(\mathcal{D}=(V,\mathcal{B})\), where \(\mathcal{B}\) subset of the set all \(k\)-dimensional subspaces \(V\), with property that each \(t\)-dimensional \(V\) contained in precisely \(\lambda\) elements \(\mathcal{B}\). Subspace designs are \(q\)-analogues balanced incomplete...

We consider the mean prediction error of a classification or regression procedure as well as its cross-validation estimates, and investigate the variance of this estimate as a function of an arbitrary cross-validation design. We decompose this variance into a scalar product of coefficients and certain covariance expressions, such that the coefficients depend solely on the resampling design, and...

Some constructions of balanced arrays of strength two are provided by use of rectangular designs, group divisible designs, and nested balanced incomplete block designs. Some series of such arrays are also presented as well as orthogonal arrays, with illustrations. # 2002 Wiley Periodicals, Inc. J Combin Designs 10: 303–312, 2002; Published online in Wiley InterScience (www.interscience.wiley.co...

A Kirkman triple system of order v, whose point set is consecutively numbered, is called smooth, if for each parallel class there is a number d, such that each triple of the parallel class forms an arithmetic progression modulo v with common difference d. It will be shown that smooth Kirkman triple systems of order v exist, if and only if v is a power of 3. 1 Smooth Kirkman triple systems The f...

Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.

1. Introduction Resolvable designs, though introduced in the combinatorial context, have found their utility in field experiments. The concept of resolvability is due to Bose (1942) who defined this for a balanced incomplete block (BIB) design. A BIB design is an arrangement of v treatments into b blocks such that each block contains k (< v) distinct treatments, each treatment appears in r bloc...

August 29, 2013 Type Package Title Basic functions for supporting an implementation of best-worst scaling Version 0.1-0 Date 2013-05-21 Author Hideo Aizaki Maintainer Hideo Aizaki Description This package provides three basic functions that support an implementation of object case (Case 1) best-worst scaling: one for converting a two-level orthogonal main-effect design/bala...

BIBD (balanced incomplete block design) is instrumental in design of experiments. This is usually constructed using algebraic tools such as finite projective (or affine) algebra or difference sets. Recently, heuristic algorithms have been tried, including artificial neural networks, simulated annealing, and local search method. In this paper, we present a novel approach to construct BIBDs that ...

In this paper, we prove two new combinatorial characterizations of authentication codes. Authentication codes without secrecy are characterized in terms of orthogonal arrays; and general authentication codes are characterized in terms of balanced incomplete block designs.