Document Type

Article

Publication Date

2001

DOI

10.1016/s0012-365x(00)00332-0

Publication Title

Discrete Mathematics

Volume

231

Issue

1-3

Pages

351-389

Abstract

If the blocks of a balanced incomplete block design (BIBD) with v treatments and with parameters (v; b1;r;k1) are each partitioned into sub-blocks of size k2, and the b2 =b1k1=k2 sub-blocks themselves constitute a BIBD with parameters (v; b2;r;k2), then the system of blocks, sub-blocks and treatments is, by de4nition, a nested BIBD (NBIBD). Whist tournaments are special types of NBIBD with k1 =2k2= 4. Although NBIBDs were introduced in the statistical literature in 1967 and have subsequently received occasional attention there, they are almost unknown in the combinatorial literature, except in the literature of tournaments, and detailed combinatorial studies of them have been lacking. The present paper therefore reviews and extends mathematical knowledge of NBIBDs. Isomorphism and automorphisms are defined for NBIBDs, and methods of construction are outlined. Some special types of NBIBD are de4ned and illustrated. A first-ever detailed table of NBIBDs with v⩽16, r⩽30 is provided; this table contains many newly discovered NBIBDs. © 2001 Elsevier Science B.V. All rights reserved.

Comments

Web of Science: "Free full-text from publisher- Elsevier open archive."

© 2001 Elsevier Science B.V. All rights reserved.

Original Publication Citation

Morgan, J. P., Preece, D. A., & Rees, D. H. (2001). Nested balanced incomplete block designs. Discrete Mathematics, 231(1-3), 351-389. doi:10.1016/s0012-365x(00)00332-0

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