Abstract
Baker ( Discrete Math., 15 (1976), 205–211) has shown that there exists a packing of the lines of each odd dimensional projective space over the field of two elements as a corollary to a theorem asserting the existence of a 2-resolution of the Steiner quadruple system of planes in an even dimensional affine space over the field of two elements. Two packings are orthogonal if any two of their spreads have at most one line in common. A variation of the previous construction gives alternate packings so that, for example, the existence of orthogonal packings of PG 2 m − 1 (2) when three does not divide 2 m − 1 can be demonstrated.
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