The modest state of knowledge .
k\g	5	6	7	8	9	10	11	12	13	14	15
3	10	14	24	30	58	70	112	126	272	384	620
4	19	26	67	80	318			728
5	30	42	152	170				2730
6	40	62	294	312				7812
7	50	90
8	80	114		800				39216
9	98	146		1170				74898
10	126	182		1640				132860
11	160	240
12	203	266		2928				354312
13	240
14	312	366		4760				804468
15	504
16	602

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This is the current state-of-the-art. Each number is a link to an actual graph of the stated order; this is the currently smallest known such graph. Values that are known to be sharp - in the most  cases because they either meet the Moore bound or are small enough that exhaustive searches  have been done, are in red.