5-designs in affine spaces

William O’Bannon Alltop

Vol. 39 (1971), No. 3, 547–551

DOI: 10.2140/pjm.1971.39.547

Abstract

The n-dimensional affine group over GF(2) is triply transitive on 2ⁿ symbols. For n ≧ 4,4 ≦ k ≦ 2ⁿ⁻¹, 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