Geodesic
On Balanced Incomplete Block Designs with Large Number of Elements
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 61-65

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Hanani, Haim. On Balanced Incomplete Block Designs with Large Number of Elements. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 61-65. doi: 10.4153/CJM-1970-008-0
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