The tables below give the sizes of the best constructions of
difference triangle sets
known. Following each entry is a pointer to
the appropriate reference in the list below the table.
References are generally the first (known to me) to find an example
of the given size.
Values
known to be optimal are linked to the appropriate place in a
separate list of
optimal difference triangle sets.
Last update July 2, 2004.
References for the tables above.

T  trivial


WB  Wallace C. Babcock

W. C. Babcock, "Intermodulation Interference in Radio Systems", Bell
System Technical Journal, 1953, p. 6373.

TS1  T. Skolem

T. Skolem, "On certain distributions of integers in pairs with given
differences", Math. Scand., 6(1958), p. 5768.
(considered more restrictive problem)

TS2  T. Skolem

T. Skolem, "Some Remarks on the triple systems of Steiner",
Math. Scand., 6(1958), p. 273280.
(considered more restrictive problem)

RD  Roy O. Davis

R. O. Davis, "On Langford's Problem (II)", Math. Gazette, 43(1959), p.
253255.
(considered more restrictive problem, see also
EO
)

EO  Edward S. O'Keefe

E. S. O'Keefe, "Verification of a conjecture of Th. Skolem", Math.
Scand., 9(1961), p. 8082.
(considered more restrictive problem)

RB  John P. Robinson and Arthur J. Bernstein

J. P. Robinson and A. J. Bernstein, "A class of binary recurrent codes
with limited error propagation", IEEE Transactions on Information
Theory, IT13(1967), p. 106113.

WM  William Mixon (unpublished, cited in)

M. Gardner, "Mathematical games", Scientific American, June 1972,
p. 116118.

BBR1  F. Biraud, E. J. Blum and J. C. Ribes

F. Biraud, E. J. Blum and J. C. Ribes, "On optimum synthetic linear
arrays with application to radioastronomy", IEEE Transactions on
Antennas and Propagation, 22(1974), p. 108109.

BBR2  F. Biraud, E. J. Blum and J. C. Ribes
(unpublished, quoted in)

D. G. Rogers, "Addition theorems for perfect systems of difference
sets", J. London Math. Soc., 23(1981), p. 385395.

BRB  E. J. Blum, J. C. Ribes and F. Biraud

E. J. Blum, J. C. Ribes and F. Biraud, "Some new possibilities of
optimium synthetic linear arrays for radioastronomy", Astronomy and
Astrophysics, 41(1975), p. 409411.

BKT  J.C. Bermond, A. Kotzig and J. Turgeon

J.C. Bermond, A. Kotzig and J. Turgeon, "On a combinatorial problem
of antennas in radioastronomy", in Proceedings 18th Hungarian
Combinatorial Colloquium (NorthHolland, Amsterdam, 1976), p.135149.
(using a result in BRB .)

PL  Philip J. Laufer

P. J. Laufer, "Regular perfect systems of difference sets of size 4
and extremal systems of size 3", Annals of Discrete Mathematics,
12(1982), p. 193201.

JR2  John P. Robinson

J. P. Robinson "Addendum to "Optimal golomb rulers""
IEEE Transactions on Computers,
C32(1983), p. 201.

GM  G. Martin

G. Martin, "Optimal convolutional selforthogonal codes with an
application to digital radio",
Proc. IEEE International Conference on Communications,
1985, p. 12491253.

KTG  F. Khansefid, H. Taylor and R. Gagliardi

F. Khansefid, H. Taylor and R. Gagliardi, "Design of (0,1) sequence
sets for pulsed coded systems",
Communications Science Institute ,
University of Southern California, Los Angeles, Rep CSI88003, 1988.

TK  Torleiv Klove

T. Klove, "Bounds and Construction for Difference Triangle Sets", IEEE
Transactions on Information Theory, 35(1989), p. 879886.

JS1  James B. Shearer

J. B. Shearer, "Some New Optimum Golomb Rulers", IEEE Transactions on
Information Theory, 36(1990), p. 183184.

JS2  James B. Shearer

J. B. Shearer, "Some New Difference Triangle Sets", IBM RC 16610,
3/5/1991.
published in part as
J. B. Shearer, "Some New Difference Triangle Sets", Journal of
Combinatorial Mathematics and Combinatorial Computing, 27(1998),
p. 6572.

JS3  James B. Shearer (unpublished)

From ongoing searches (started October 30, 1998) using a program
similar to that described in JS2 .

JS4  James B. Shearer (unpublished)

From ongoing searches (started Fall 1999)
using a program to find better difference
triangle sets by local changes.

JS5  James B. Shearer

J. B. Shearer, "Improved LP Lower Bounds for Difference Triangle Sets",
The Electronic Journal of Combinatorics, 6(1999), #R31.

CFJ  Zhi Chen, Pingzhi Fan and Fan Jin

Z. Chen, P. Fan and F. Jin, "Disjoint Difference Triangle Sets", IEEE
Transactions on Information Theory, IT38(1992), p. 518522.

ZC  Zhi Chen

Z. Chen, "Further Results on Difference Triangle Sets", IEEE
Transactions on Information Theory, IT40(1994), p. 12681270.

AL  Alan C. H. Ling

Ling, Alan C. H.,
"Difference Triangle Sets From Affine Planes",
IEEE Transactions on Information Theory,
IT48(2002), p. 23992401.
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