More about maximal (n, r)-sets

Consider a finite r-dimensional projective space PG(r, s) based on the Galois field GF(s) where s is prime or power of a prime. A set of n distinct points in PG(r, s), no t linearly dependent, is said to be maximal or complete if it is not contained in any other set with n* points with n* > n. The number of points in a maximal set is denoted by mt(r + 1, s). The purpose of this paper is to improve the existing bounds for m5(r + 1, s) for r ≥ 5 and s ≥ 5 (odd). The investigation of maximal sets in certain relationships of t, r and s yields parity check matrices of (r + 1) rows and n columns with elements from GF(s) satisfying the condition that no t columns are linearly dependent. This problem has applications to coding theory and also in the theory of fractionally replicated designs. © 1972 Academic Press, Inc.

2 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/060-968-103-549-655 tex.type: [object Object]