A library of putatively
optimal coverings of the sphere with n equal caps.
How should one place n points on a sphere so as to
minimize the maximum distance of any point on the sphere
from the closest one of the n points?
This maximum distance is called the covering radius.
We give putatively optimal coverings for n = 4, ..., 130.
Coverings by points on a sphere
Copyright R. H. Hardin, N. J. A. Sloane & W. D. Smith, Feb 1994
dim npts covering radius (degrees) 3 4 70.5287794 3 5 63.4349488 3 6 54.7356103 3 7 51.0265527 3 8 48.1395291 3 9 45.8788878 3 10 42.3078266 3 11 41.4271960 3 12 37.3773681 3 13 37.0685427 3 14 34.9379270 3 15 34.0399001 3 16 32.8988128 3 17 32.0929328 3 18 31.0131718 3 19 30.3686748 3 20 29.6230958 3 21 28.8244768 3 22 27.8100588 3 23 27.4818687 3 24 26.8126364 3 25 26.3287855 3 26 25.8449223 3 27 25.2509549 3 28 24.6589489 3 29 24.3683986 3 30 23.8787580 3 31 23.6119921 3 32 22.6904804 3 33 22.5905116 3 34 22.3314637 3 35 22.0725569 3 36 21.6994390 3 37 21.3100299 3 38 21.0698584 3 39 20.8511244 3 40 20.4721353 3 41 20.3177152 3 42 20.0480917 3 43 19.8428333 3 44 19.6375705 3 45 19.4207407 3 46 19.1586113 3 47 18.9924594 3 48 18.6892566 3 49 18.5926796 3 50 18.3000226 3 51 18.1990011 3 52 18.0544758 3 53 17.8845734 3 54 17.6791447 3 55 17.5222392 3 56 17.3501139 3 57 17.1758476 3 58 17.0199610 3 59 16.9034031 3 60 16.7719330 3 61 16.6391845 3 62 16.4906596 3 63 16.3679364 3 64 16.1940190 3 65 16.1114061 3 66 15.9550615 3 67 15.8581808 3 68 15.7236959 3 69 15.5950401 3 70 15.4951288 3 71 15.3918904 3 72 15.1445321 3 73 15.1164437 3 74 15.0311866 3 75 14.9454277 3 76 14.8539208 3 77 14.7449905 3 78 14.6550577 3 79 14.5627673 3 80 14.4503042 3 81 14.3767803 3 82 14.2863117 3 83 14.2239571 3 84 14.1157901 3 85 14.0452618 3 86 13.9626271 3 87 13.8849703 3 88 13.7904978 3 89 13.7120948 3 90 13.6208737 3 91 13.5633748 3 92 13.4878634 3 93 13.4258226 3 94 13.3486301 3 95 13.2858097 3 96 13.2112886 3 97 13.1421390 3 98 13.0644481 3 99 12.9972791 3 100 12.9360973 3 101 12.8693268 3 102 12.8065480 3 103 12.7396985 3 104 12.6710007 3 105 12.6206479 3 106 12.5580705 3 107 12.4984676 3 108 12.4268411 3 109 12.3823879 3 110 12.3000527 3 111 12.2463574 3 112 12.1906904 3 113 12.1475147 3 114 12.0965651 3 115 12.0509312 3 116 11.9886435 3 117 11.9433897 3 118 11.8858175 3 119 11.8437244 3 120 11.7866486 3 121 11.7339186 3 122 11.6770714 3 123 11.6364348 3 124 11.5887833 3 125 11.5384928 3 126 11.4894028 3 127 11.4535231 3 128 11.4068506 3 129 11.3563380 3 130 11.3165625