There is no 2‐(22, 8, 4) block design

Bilous, R. T.; Lam, Clement; Thiel, L.; Li, P. C.; Rees, Glynda; Radziszowski, Stanisław; Holzmann, W. H.; Kharaghani, Hadi

doi:10.1002/jcd.20132

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Quasi-residual Designs1

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Cited by 3 publications

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“…This The designs that do exist can be realized as residuals of symmetric designs, and the status of those with question marks is at present unknown. The ∄-marked (22,33,12,8,4) has recently been shown not to exist [1] (see also the exposition in [16]). Designs with the parameters marked with ⋪ do exist, but none are residuals of symmetric designs, the needed designs being ruled out by the Bruck-Ryser-Chowla theorem.…”

Section: Quasi-residual Designsmentioning

confidence: 99%

Design Lines

Ward

2010

Preprint

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The two basic equations satisfied by the parameters of a block design define a three-dimensional affine variety D in R 5 . A point of D that is not in some sense trivial lies on four lines lying in D. These lines provide a degree of organization for certain general classes of designs, and the paper is devoted to exploring properties of the lines. Several examples of families of designs that seem naturally to follow the lines are presented.

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