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On Balanced Incomplete Block Designs with Large Number of Elements

Published online by Cambridge University Press:  20 November 2018

Haim Hanani
Haim Hanani*
Affiliation:
Technion–Israel Institute of Technology, Technion City, Haifa
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A balanced incomplete block design (BIBD) B[k, λ; v] is an arrangement of v distinct elements into blocks each containing exactly k distinct elements such that each pair of elements occurs together in exactly λ blocks.

The following is a well-known theorem [5, p. 248].

THEOREM 1. A necessary condition for the existence of a BIBD B[k, λ,v] is that

(1)

It is also well known [5] that condition (1) is not sufficient for the existence of B[k, λ; v].

There is an old conjecture that for any given k and λ condition (1) may be sufficient for the existence of a BIBD B[k, λ; v] if v is sufficiently large. It is attempted here to prove this conjecture in some specific cases.

There is an old conjecture that for any given k and X condition (1) may be sufficient for the existence of a BIBD B[k, λ; v] if v is sufficiently large. It is attempted here to prove this conjecture in some specific cases.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 61 - 65
Copyright
Copyright © Canadian Mathematical Society 1970

References

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