Mutually unbiased bases in composite dimensions

Find the most mutually unbiased bases possible in dimension d when d is not a prime power; for d = 6 it is 3, 4 or 5, and a claimed proof of 3 awaits checking.

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1	{
2	"domain": "physics-astronomy",
3	"topics": [
4	"quantum-information",
5	"combinatorics"
6	],
7	"type": "proof",
8	"also": [
9	"construction"
10	],
11	"source": {
12	"key": "qiqcop",
13	"name": "QIQCOP Zoo",
14	"url": "https://qiqc-op.com/problem/op_c9c62042b15fcb06/",
15	"id": "op_c9c62042b15fcb06",
16	"curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
17	"poser": "Gerhard Zauner (conjecture that μ(6) = 3)",
18	"status": "unsolved",
19	"as_of": "2026-10-20",
20	"catalog": "0521c19bbd38"
21	},
22	"review": true,
23	"approval": "first-time"
24	}