The number of designs with geometric parameters grows exponentially
It is well-known that the number of 2-designs with the parameters of a classical point-hyperplane design PGn-1(n, q) grows exponentially. Here we extend this result to the number of 2-designs with the parameters of PGd (n, q), where 2 ≤ d ≤ n − 1. We also establish a characterization of the classical geometric designs in terms of hyperplanes and, in the special case d = 2, also in terms of lines. Finally, we shall discuss some interesting configurations of hyperplanes arising in designs with geometric parameters.
Designs, Codes and Cryptography
The number of designs with geometric parameters grows exponentially.
Designs, Codes and Cryptography,
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