Geodesic
On a theorem of Beck
Glasgow mathematical journal, Tome 26 (1985), pp. 195-201

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Let T(N) be the least integer such that one can assign ±l's to any N points in the unit square so that the sum of these values in any rectangle with sides parallel to those of the square have absolute value at most T(N). In [1] Beck showed, among other results, that (for N≥2). 
Roth, K. F. On a theorem of Beck. Glasgow mathematical journal, Tome 26 (1985), pp. 195-201. doi: 10.1017/S0017089500006182
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[1] 1.Beck, József, Balanced Two-Colorings of Finite Sets in the Square I, Combinatorica 1 (1981), 327–335. Google Scholar | DOI

[2] 2.Schmidt, W. M., Irregularities of Distribution VII, Acta Arith., 21 (1972), 45–50. Google Scholar | DOI

[3] 3.Schmidt, W. M., Irregularities of Distribution X, Number Theory and Algebra (ed. Zassenhaus, H., Academic Press, 1977), 311–329. Google Scholar

[4] 4.Halász, G., On Roth's method in the theory of irregularities of point distributions, Recent Progress in Analytic Number Theory, Vol. 2 (eds. Halberstam, H. and Hooley, C., Academic Press, 1981), 79–94. Google Scholar

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