Nature Communications

Table 2 List of HYPER designs H_n,m,q considered.

From: Group testing via hypergraph factorization applied to COVID-19

q = 1				q = 2									q = 3
n	m	n	m	n	m		n	m		n	m		n	m		n	m		n	m
4	1	384	1	12	6	*	96	64	*	384	42		12	6		96	48	*	400	48	*
8	1	384	2	12	12		144	30		384	44		12	12	*	96	60		400	60
12	6	384	3	20	12		192	6	*	384	46	*	12	18		96	90		400	90
20	10	384	4	20	20		192	12		384	48		20	12	*	144	30		400	192	*
40	10	384	6	24	6	*	192	20		384	64	*	20	18		180	90		400	282
40	20	384	8	24	12		192	24		384	96		20	30		192	6		400	384	*
44	11	384	12	40	12		192	40		384	192		24	6		192	12	*	400	390
44	22	384	16	40	20		192	44		384	288		24	12	*	192	18		720	90
48	12	384	24	40	40		192	48		400	12		40	12	*	192	24	*	768	12	*
48	16	384	32	44	12		192	64	*	400	20		40	18		192	30		768	24	*
48	24	384	48	44	20		192	192		400	40		40	30		192	42		768	48	*
64	8	384	64	44	40		192	96		400	44		40	42		192	48	*	1440	90
64	16	384	96	44	44		288	12		400	48		40	48	*	192	60		1536	24	*
64	32	384	128	48	6	*	288	20		400	64	*	40	60		192	90		1536	48	*
80	20	384	192	48	12		288	30		400	96		44	12	*	192	192	*	2880	90
96	1	400	10	48	20		288	40		400	192		44	18		288	12	*	3072	48	*
96	2	400	20	48	24		288	44		400	288		44	30		288	18		5760	90
96	3	400	40	48	40		288	48		400	384		44	42		288	30
96	4	400	50	48	44		288	64	*	768	12		44	48	*	288	42
96	6	400	80	48	48		288	96		768	24		44	60		288	48	*
96	8	400	100	64	12		288	192		768	48		48	6		288	60
96	12	400	200	64	20		384	4	*	768	96		48	12	*	288	90
96	16			64	40		384	6	*	1536	24		48	18		288	192	*
96	24			64	44		384	8	*	1536	48		48	24	*	288	282
96	32			64	48		384	10	*	1536	96		48	30		360	90
96	48			64	64	*	384	12		3072	48		48	42		384	6
100	20			96	4	*	384	14	*	3072	96		48	48	*	384	12	*
192	12			96	6	*	384	16	*	6144	96		48	60		384	18
192	16			96	8	*	384	18	*				64	12	*	384	24	*
192	32			96	10	*	384	20					64	18		384	30
192	48			96	12		384	22	*				64	30		384	42
192	64			96	14	*	384	24					64	42		384	48	*
192	96			96	16	*	384	26	*				64	48	*	384	60
288	12			96	18	*	384	28					64	60		384	90
288	18			96	20		384	30					96	6		384	192	*
288	36			96	22	*	384	32	*				96	12	*	384	282
288	48			96	24		384	34	*				96	18		400	12	*
288	96			96	40		384	36					96	24	*	400	18
288	144			96	44		384	38	*				96	30		400	30
360	40			96	48		384	40					96	42		400	42

HYPER was optimized across the following set of design parameters. Asterisks (*) denote the restricted set of parameters that are available for Reed-Solomon Kautz-Singleton (RS-KS) code-based designs (see the Supplementary Material).

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