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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 L1-norm. 0
1, 2, 8, 18, 40 (list; graph; refs; listen; history; text; internal format)
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^(r-1))*A(n,2^r,2^r); compare the Edel-Rains-Sloane paper and the tables of And and Andw mentioned here - N. J. A. Sloane, Oct 12 2001. This gives 40 in 4-D, 256 in 8-D (found also by Blokhuis), 2144 in 16-D, 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

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Last modified February 28 08:22 EST 2021. Contains 341695 sequences. (Running on oeis4.)