Calderbank, AR; Fishburn, PC, *Maximal three-independent subsets of {0, 1, 2}*^{n},
Designs, Codes and Cryptography, vol. 4 no. 4
(1994),
pp. 203-211 [doi] .
**Abstract:**

*We consider a variant of the classical problem of finding the size of the largest cap in the r-dimensional projective geometry PG(r, 3) over the field IF3 with 3 elements. We study the maximum size f(n) of a subset S of IF3n with the property that the only solution to the equation x1+x2+x3=0 is x1=x2=x3. Let cn=f(n)1/n and c=sup{c1, c2, ...}. We prove that c>2.21, improving the previous lower bound of 2.1955 ... © 1994 Kluwer Academic Publishers.*