

A064705


Maximal number of vectors u_1, u_2, ... in R^n with u_i = 1 and u_i  u_j >= 1 for i, j distinct, where  is L1norm.


0




OFFSET

0,2


COMMENTS

L1 norm of (a,b,c,...) = a+b+c+...
A lower bound if n = 2^m >= 4: a(n) >= 2n^2 + Sum_{r=2..[log_2 n]} A(2^r,2^(r1))*A(n,2^r,2^r); compare the EdelRainsSloane paper and the tables of And and Andw mentioned here  N. J. A. Sloane, Oct 12 2001. This gives 40 in 4D, 256 in 8D (found also by Blokhuis), 2144 in 16D, etc.


LINKS

Table of n, a(n) for n=0..4.
A. E. Brouwer, Tables of general binary codes
A. E. Brouwer, Bounds for binary constant weight codes
Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128, Elect. J. Combin.
Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128


EXAMPLE

It is easier to take the norm to be 2. For n=2: { +2 0, 0 +2, +1 +1 }; for n=3: { 200 etc. (6) and 110 etc. (12) }; for n=4: { 2000 etc. (8), 1100 etc. (24), .5 .5 .5 .5 etc. (8) }.


CROSSREFS

Sequence in context: A198014 A252592 A188577 * A220909 A058858 A236633
Adjacent sequences: A064702 A064703 A064704 * A064706 A064707 A064708


KEYWORD

nonn,more


AUTHOR

Aart Blokhuis (aartb(AT)win.tue.nl), Oct 11 2001


STATUS

approved



