Vol. 39, No. 3, 1971

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5-designs in affine spaces

William O’Bannon Alltop

Vol. 39 (1971), No. 3, 547–551
Abstract

The n-dimensional affine group over GF(2) is triply transitive on 2n symbols. For n 4,4 k 2n1, any orbit of k-subsets is a 3 (2n,k,λ) design. In this paper a sufficient condition that such a design be a 4-design is given. It is also shown that such a 4-design must always be a 5-design. A 5-design on 256 varieties with block size 24 is constructed in this fashion.

Mathematical Subject Classification 2000
Primary: 05B05
Milestones
Received: 16 February 1970
Published: 1 December 1971
Authors
William O’Bannon Alltop