This question, also known as problem of the "enimated dictators", was first asked by the biologist Tammes, who studied the boundaries of pollen grains. But it can be also viewed as energy-sum-problem. It is:

m:	max (l∞)
e:	1/| pi,pj|

The problem had been completely solved for N = 4,..,12,24. Very good arrangements are known for N < 122 due to the work of B.W.Clare and D.L.Kepert as well as D.Kottwitz. They approaches the solution of Tammes' problem by the solution of energy-sum-problems for α → -∞.

T.Tarnai and Zs. Gaspar developted an optimization algorithm using bars:
To a given point-arrangement a system of bars is constructed. This system is heated continuously and occuring tensions are reduced by adding new bars until the system is rigid. The algorithm finishes when no further change or improvement is possible.

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Lagerungen in der Ebene, auf der Kugel und im Raum
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The Problem of Tammes for n = 11
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The Closest Packing of Equal Circles on a Sphere
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The Problem of Tammes for n = 10
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www.research.att.com/~njas/packings/

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The Densest Packing of Equal Circles on a Sphere
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Arrangement of 24 Circles on a Sphere
Math. Ann. 144 (1961), 17-48

[ 9] Schütte, K.; v.d. Waerden, B.L.

Auf welcher Kugel haben 5,6,7,8 oder 9 Punkte mit Mindestabstand Eins Platz ?
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On the Origin Number and Arrangement of the Places of Exits on the Surface of Pollengrains
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Improved Packing of Equal Circles on a Sphere and Rigidity of its Graph Math. Proc. Cambridge Phil. Soc. 93 (1983), 2, 191-218

[12] v.d. Waerden:

Punkte auf der Kugel. Drei Zusätze Math. Ann. 125 (1952), 213-222