What question did this study set out to answer?

March 28, 2026

1‐Rotational Balanced Incomplete Block Designs With Block Size Four and Arbitrary Index

Key Points

The study aims to identify necessary and sufficient conditions for the existence of 1-rotational balanced incomplete block designs (BIBDs) with a block size of four.
Determined conditions for existence of BIBDs with block size four and arbitrary index.
Analyzed the spectrum of 1-rotational BIBDs based on mathematical criteria.
Utilized combinatorial theory to support findings.
Established clear existence conditions for BIBDs based on specific parameters.
Demonstrated that a 1-rotational BIBD exists under certain mathematical restrictions.

Abstract

ABSTRACT The necessary and sufficient conditions for the existence of 1‐rotational balanced incomplete block designs with block size four and index unity have been determined to be and J. Comb. Theory, Ser. A 206 (2024) 105890. This work completely determines the existence spectrum of 1‐rotational balanced incomplete block designs with block size four and any index . To be specific, for and , there exists a 1‐rotational BIBD if and only if , and .

Bookmark

1‐Rotational Balanced Incomplete Block Designs With Block Size Four and Arbitrary Index

Key Points

Abstract

Cite This Study