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Group Divisible Designs with Block Size Four and Group Type inline image for inline image

Authors


  • Contract grant sponsor: Research supported by the National Outstanding Youth Science Foundation of China under Contract Grant Number: 10825103; Contract grant sponsor: National Natural Science Foundation of China under, Contract Grant Number: 61171198; Contract grant sponsor: Specialized Research Fund for the Doctoral Program of Higher Education.

Abstract

Nonuniform group divisible designs (GDDs) have been studied by numerous researchers for the past two decades due to their essential role in the constructions for other types of designs. In this paper, we investigate the existence problem of inline image-GDDs of type inline image for inline image. First, we determine completely the spectrum of inline image-GDDs of types inline image and inline image. Furthermore, for general cases, we show that for each inline image and inline image, a inline image-GDD of type inline image exists if and only if inline image, inline image and inline image, except possibly for inline image, inline image and inline image.

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