
COMMENTS

a(n) >= n^2n+1 by a volume bound. A difference set construction by Singer shows that equality holds when n1 is a prime power. When n is a prime power, a difference set construction by Bose shows that a(n) <= n^21. By computation, equality holds in the latter bound at least for 7, 11, 13 and 16.
From Fausto A. C. Cariboni, Aug 13 2017: (Start)
Lexicographically first basis that yields a(n) for n=15..18:
a(15) = 255 from {0,1,3,7,15,26,31,53,63,98,107,127,140,176,197}
a(16) = 255 from {0,1,3,7,15,26,31,53,63,98,107,127,140,176,197,215}
a(17) = 273 from {0,1,3,7,15,31,63,90,116,127,136,181,194,204,233,238,255}
a(18) = 307 from {0,1,3,21,25,31,68,77,91,170,177,185,196,212,225,257,269,274}
(End)
Such sets are also known as modular Golomb rulers, or circular Golomb rulers.  Andrey Zabolotskiy, Sep 11 2017


LINKS

Table of n, a(n) for n=1..18.
Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See p. 162.
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382404 (v_delta).
H. Haanpaa, A. Huima and P. R. J. Ostergard, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 12, 99106.
H. Haanpaa, A. Huima and P. R. J. Ostergard, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 12, 99106. [Annotated scanned copies of four pages only from preprint of paper above]
Z. Skupien, A. Zak, Pairsums packing and rainbow cliques, in Topics In Graph Theory, A tribute to A. A. and T. E. Zykovs on the occasion of A. A. Zykov's 90th birthday, ed. R. Tyshkevich, Univ. Illinois, 2013, pages 131144, (in English and Russian).
