Group divisible designs with block size four and type g^um¹—II

Forbes, A. D. (2019). Group divisible designs with block size four and type g^um¹—II. Journal of Combinatorial Designs, 27(5) pp. 311–349.

DOI: https://doi.org/10.1002/jcd.21650

Abstract

We show that the necessary conditions for the existence of group divisible designs with block size four (4‐GDDs) of type g^um¹ are sufficient for g ≡ 0 (mod h), h = 39, 51, 57,69, 87, 93, 111, 123 and 129, and for g = 13, 17, 19, 23, 25,29, 31 and 35. More generally, we show that for g ≡ 3 (mod 6), the possible exceptions occur only when u = 8, and there are no exceptions at all if g/3 has a divisor d>1 such that d ≡ 1 (mod 4) or d is a prime not greater than 43. Hence there are no exceptions when g ≡ 3 (mod 12). Consequently, we are able to extend the known spectrum for g ≡ 1 and 5 (mod 6). Also, we complete the spectrum for 4‐GDDs of type (3α)⁴(6α)¹(3b)¹.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 59083
• Item Type
• Journal Item
• ISSN
• 1520-6610
• Keywords
• double group divisible design; 4‐GDD; group divisible design
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2019 Wiley Periodicals, Inc.
• Related URLs
• • http://oro.open.ac.uk/55034/(Publication)
• SWORD Depositor
• Jisc Publications-Router
• Depositing User
• Jisc Publications-Router