> > Start with 500 random numbers.
> > Throw out the ones that violate the tests.
> > Hope that you are left with enough (361).
> >
> > This actually worked all the way down to 15-bit numbers.
>
> Neat. Was the 15-bit version for 81 values or 361? At the risk of
> putting my foot in my mouth, I don't think there exist 361 15-bit
> numbers that satisfy minimum requirements (if the floating-point
> average of any four code values is a code value, then the four code
> values are identical).

It was 361 values.  So either you are wrong or I have a bug.  I
probably have a bug.  Here's the list.  If it violates the rules,
please let me know.

14
56
81
155
354
383
414
448
467
472
513
519
520
591
619
633
732
766
873
875
949
1025
1058
1129
1148
1153
1207
1221
1230
1281
1283
1401
1546
1712
1720
1777
1791
1816
1936
2011
2061
2104
2217
2335
2367
2418
2456
2466
2502
2553
2792
2846
2898
2958
3022
3047
3051
3232
3295
3410
3702
3867
4178
4227
4247
4358
4382
4542
4646
4650
4683
4877
4895
4917
4968
4977
5396
5398
5408
5477
5641
5688
5702
5707
5730
5791
5875
6010
6124
6172
6188
6379
6438
6447
6452
6599
6607
6609
6633
6653
6808
6833
6852
6867
6876
6962
6996
7085
7108
7155
7311
7396
7489
7494
7672
7795
7863
7894
7908
8115
8192
8244
8484
8527
8581
8687
8715
8886
8941
8982
9101
9105
9217
9259
9500
9576
9708
9742
9750
9803
9808
9921
9967
10093
10094
10138
10232
10293
10332
10369
10381
10616
10617
10646
10739
10944
11032
11181
11239
11280
11670
11677
11679
11778
11912
12101
12126
12188
12418
12439
12451
12534
12705
12731
12752
12922
12973
13001
13009
13022
13069
13189
13203
13279
13375
13383
13654
13669
13858
13943
14047
14147
14263
14380
14414
14529
14618
14646
14766
14809
14817
14941
14975
14993
15051
15161
15192
15207
15499
15517
15540
15554
15628
15686
15689
15837
15840
15874
15954
16063
16084
16091
16096
16168
16199
16335
16350
16416
16500
16580
16775
16814
17089
17227
17256
17564
17706
17829
17848
18227
18354
18422
18611
18614
18634
18741
18935
18953
18962
19034
19074
19102
19180
19234
19314
19351
19692
19694
19842
19869
19935
20228
20254
20320
20428
20540
20694
20728
20729
21021
21212
21269
21442
21538
21764
21824
21840
21918
21986
22005
22103
22174
22204
22289
22320
22353
22359
22759
22865
22960
22980
23127
23145
23199
23292
23298
23364
23392
23481
23564
23645
23664
23720
23829
24143
24184
24426
24428
24496
24710
24872
25001
25294
25443
25453
25615
25719
25907
26092
26452
26593
26865
27106
27186
27386
27428
27532
27628
27723
27749
27919
27954
28243
28573
28672
28681
28691
28699
28749
28878
29040
29113
29141
29358
29565
29627
29960
29977
30607
30675
30917
31127
31348
31374
31679
32000
32033
32050
32162
32443
32444
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