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Group divisible designs with block-size four. (English) Zbl 0371.62105

Summary: It is proved that the obvious necessary conditions for the existence of a group divisible design with \(k = 4\) are sufficient, except for the cases corresponding to the non-existing transversal designs \(T[4, 1; 2]\) and \(T[4, 1; 6]\).
The paper is identical to Section 6.3 of H. Hanani’s paper [Discrete Math. 11, 255–369 (1975; Zbl 0361.62067).

MSC:

62K05 Optimal statistical designs
05B30 Other designs, configurations

Citations:

Zbl 0361.62067
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Full Text: DOI

Online Encyclopedia of Integer Sequences:

The coding-theoretic function A(n,6,4).

References:

[1] Hanani, H., Balanced incomplete block designs and related designs, Discrete Math., 11, 255-369 (1975) · Zbl 0361.62067
[2] Tarry, G., Le problème des 36 officiers, C.R. Assoc. Fr. Av. Sci., 2, 170-203 (1901) · JFM 32.0219.04
[3] Hanani, H.; Ray-Chaudhuri, D. K.; Wilson, R. M., On resolvable designs, Discrete Math., 3, 343-357 (1972) · Zbl 0263.05016
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