hexagonMini

Trying to find an convex hexagon without inner points in a random pointcloud.

We know that 29 points is not enough to have an empty hexagon (Mark Oversmars, Utrecht University) and that 463 *are* enough (demonstrated in 2007 by Vitaliy Koshelev, Moscow University). May we find a set of more than 29 non-aligned points without empty convex hexagon? Pour la Science #376 paper

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N	quads min	pentagons min
6	3	0
7	6	0
8	10	0
9	18	1
10	26	1
11	37	6
12	50	7
13	74	16
14	91	18
15	112	22
16	132	26

N	quads min	pentagons min
6	3	0
7	6	0
8	10	0
9	18	1
10	26	1
11	37	6
12	50	7
13	74	16
14	91	18
15	112	22
16	132	26

N	quads min	pentagons min
6	3	0
7	6	0
8	10	0
9	18	1
10	26	1
11	37	6
12	50	7
13	74	16
14	91	18
15	112	22
16	132	26

N	quads min	pentagons min
6	3	0
7	6	0
8	10	0
9	18	1
10	26	1
11	37	6
12	50	7
13	74	16
14	91	18
15	112	22
16	132	26