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We study the placement of n balls into n bins where balls and bins arerepresented as two vector spaces over Z 2 . The placement is done according toa linear transformation between the two vector spaces. We analyze the expectedsize of a largest bin. The only currently known upper bound is O(log n log logn) by Alon et al. and holds for placing n log n balls into n bins. We show thatthis bound can be improved to O(log n) in the case when n balls are placed inton bins. We use the same basic technique as Alon et al. but give a tighteranalysis for this case.

A Note On the Size of Largest Bins Using Placement With Linear Transformations