Bibliography

This page contains some references that have been used in constructing these tables.

Difference Set Surveys

There is a large literature on difference sets, from which I've pulled most of the results in this database. Earlier surveys and tables of difference set parameters include:

[Hal56] Marshall Hall Jr. A survey of difference sets. Proc. AMS, 7:975-986, 1956.
Abelian difference sets with k ≤ 50.
[Bau71] Leonard D. Baumert. Cyclic Difference Sets, volume 182 of Lecture Notes in Mathematics. Springer-Verlag, 1971.
Cyclic difference sets with k ≤ 100.
[BG03] Leonard D. Baumert and Daniel M. Gordon On the existence of cyclic difference sets with small parameters In High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communication, pages 61-68. AMS, Providence, 2004.
[Lan83] Eric S. Lander. Symmetric Designs: An Algebraic Approach, volume 74 of LMS Lecture Note Series. Cambridge, 1983.
Abelian difference sets with k ≤ 50.
[Kop89] L. E. Kopilovich. Difference sets in noncyclic abelian groups. Cybernetics, 25(2):153-157, 1989.
Abelian difference sets with 50 ≤ k ≤ 100.
[LS97] A. Vera Lopez and M. A. Garcia Sanchez. On the existence of abelian difference sets with 100 < k <=150. J. Comb. Math. Com. Comp., pages 97-112, 1997.
Abelian difference sets with 100 < k ≤ 150.
[Jun92] Dieter Jungnickel. Difference sets. In Jeffrey H. Dinitz and Douglas R. Stinson, editors, Contemporary Design Theory: A Collection of Surveys, pages 241-324. Wiley, 1992.
[Smi07] Ken Smith's Difference Set Database.
all difference sets with n ≤ 15, and others. link no longer works
[Abu16] AbuGhneim Database of all (64,28,12) and (96,20,4) difference sets.

Papers on Difference Sets

The difference set database refers to results from a number of papers, listed here.

[Ara86] K. T. Arasu. (81,16,3) abelian difference sets do not exist. JCT A, 43:350-353, 1986.
[Ara88] K.T. Arasu. More missing entries in lander's table could be filled. Arch. Math., 51:188-192, 1988.
[AC01] K. T. Arasu and Yu Qing Chen. A difference set in (Z/4Z)3× Z/5Z. Des. Codes Cryptography, 23:317-324, 2001.
[ADJ+96] K. T. Arasu, James A. Davis, Jonathan Jedwab, Siu Lun Ma, and Robert L. McFarland. Exponent bounds for a family of abelian difference sets. In Proceedings of a special research quarter on Groups, difference sets, and the monster, pages 129-143, Hawthorne, NJ, USA, 1996. Walter de Gruyter & Co.
[AM98] K. T. Arasu and S. L. Ma. Abelian difference sets without self-conjugacy. Des. Codes Cryptography, 15:223-230, December 1998.
[AS92] K. T. Arasu and Surinder K. Sehgal. Some new results on abelian difference sets. Util. Math., 42:225-233, 1992.
[AS95a] K. T. Arasu and Surinder K. Sehgal. Difference sets in abelian groups of p-rank two. Des. Codes Cryptography, 5:5-12, 1995.
[AS95b] K. T. Arasu and Surinder K. Sehgal. Some new difference sets. J. Comb. Theory Ser. A, 69:170-172, 1995.
[Bau69] Leonard D. Baumert. Difference sets. SIAM J. Appl. Math., 17:826-833, 1969.
[BM14] Peter Borwein and Michael Mossinghoff. Wieferich pairs and Barker sequences II. LMS Journal of Comp. and Math., 17 (2014), pp. 24-32.
[Fen10] Tao Feng. Nonexistence of some (945,177,33)-difference sets. Ars Combinatoria, 94, 2010.
[Hug78] Daniel Hughes. Biplanes and semi-biplanes. In D. Holton and Jennifer Seberry, editors, Combinatorial Mathematics, volume 686 of Lecture Notes in Mathematics, pages 55-58. Springer Berlin / Heidelberg, 1978.
[Iia99] Joel E. Iiams. Lander's tables are complete! In A. Pott, P. V. Kumar, T. Helleseth, and D. Jungnickel, editors, Difference Sets, Sequences and Their Correlation Properties, volume 542 of NATO Science Series, pages 239-257. Springer Netherlands, 1999.
[ILS96] Joel E. Iiams, Robert A. Liebler, and Kenneth W. Smith. Difference sets in nilpotent groups with large frattini quotient: geometric methods and (375, 34, 3). In Proceedings of a special research quarter on Groups, difference sets, and the monster, pages 157-168, Hawthorne, NJ, USA, 1996. Walter de Gruyter & Co.
[Jia00] Z. Jia. On (351,126,45)-difference sets. Ars. Comb., 57:293-300, 2000.
[LS11] Siu Ka Hin Leung and Bernhard Schmidt. New restrictions on possible orders of circulant Hadamard Matrices. Des. Codes Cryptography, 64 (2011), pages 143-151.
[MS97] Siu Lun Ma and Bernhard Schmidt. Difference sets corresponding to a class of symmetric designs. Des. Codes Cryptography, pages 223-236, 1997.
[McF73] R. L. McFarland. A family of difference sets in non-cyclic groups. JCT A, 15:1-10, 1973.
[Osi11] A. S. Osifodunrin. On the existence of non-abelian (210,77,28), (336,135,54) and (496,55,6) difference sets. Disc. Math., Alg. and Appl., 3:121-137, 2011.
[Sch98] Bernhard Schmidt. Nonexistence of a (783,69,6)-difference set. Discrete Math., 178:283-285, 1998.
[Sch00] Bernhard Schmidt. Towards Ryser's conjecture. In C. Casacuberta et. al., editor, Proc. Third European Congress of Mathematics, pages 533-541. Birkhäuser, 2000.
[Tur65] R. J. Turyn. Character sums and difference sets. Pac. J. Math., 15:319-346, 1965.
[Tur68] R. J. Turyn. Sequences with small correlation. In H. B. Mann, editor, Error Correcting Codes, pages 195-228. Wiley, New York, 1968.


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