Some existence conditions for partially balanced arrays with 2 symbols

Some Conditions for Existence and Integrability

Abstract. The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions. The Fourier transform is calculated as an improper integral and the limit coincides with the Fourier transform in the distributional sense. The inver...

Existence of some signed magic arrays

Balanced nested designs and balanced arrays

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...

A New Family of Partially Balanced Incomplete Block Designs with Some Latin Square Design Properties

Double Arrays, Triple Arrays and Balanced Grids

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.