What is the smallest valid jpeg file size (in bytes)
A 1x1 grey pixel in 125 bytes using arithmetic coding, still in the JPEG standard even if most decoders can't decode it:
ff d8 : SOI
ff e0 ; APP0
00 10
4a 46 49 46 00 01 01 01 00 48 00 48 00 00
ff db ; DQT
00 43
00
03 02 02 02 02 02 03 02
02 02 03 03 03 03 04 06
04 04 04 04 04 08 06 06
05 06 09 08 0a 0a 09 08
09 09 0a 0c 0f 0c 0a 0b
0e 0b 09 09 0d 11 0d 0e
0f 10 10 11 10 0a 0c 12
13 12 10 13 0f 10 10 10
ff c9 ; SOF
00 0b
08 00 01 00 01 01 01 11 00
ff cc ; DAC
00 06 00 10 10 05
ff da ; SOS
00 08
01 01 00 00 3f 00 d2 cf 20
ff d9 ; EOI
I don't think the mentioned 134 byte example is standard, as it is missing an EOI. All decoders will handle this but the standard says it should end with one.
That file can be generated with:
#!/usr/bin/env bash
printf '\xff\xd8' # SOI
printf '\xff\xe0' # APP0
printf '\x00\x10'
printf '\x4a\x46\x49\x46\x00\x01\x01\x01\x00\x48\x00\x48\x00\x00'
printf '\xff\xdb' # DQT
printf '\x00\x43'
printf '\x00'
printf '\x03\x02\x02\x02\x02\x02\x03\x02'
printf '\x02\x02\x03\x03\x03\x03\x04\x06'
printf '\x04\x04\x04\x04\x04\x08\x06\x06'
printf '\x05\x06\x09\x08\x0a\x0a\x09\x08'
printf '\x09\x09\x0a\x0c\x0f\x0c\x0a\x0b'
printf '\x0e\x0b\x09\x09\x0d\x11\x0d\x0e'
printf '\x0f\x10\x10\x11\x10\x0a\x0c\x12'
printf '\x13\x12\x10\x13\x0f\x10\x10\x10'
printf '\xff\xc9' # SOF
printf '\x00\x0b'
printf '\x08\x00\x01\x00\x01\x01\x01\x11\x00'
printf '\xff\xcc' # DAC
printf '\x00\x06\x00\x10\x10\x05'
printf '\xff\xda' # SOS
printf '\x00\x08'
printf '\x01\x01\x00\x00\x3f\x00\xd2\xcf\x20'
printf '\xff\xd9' # EOI
and opened fine with GNOME Image Viewer 3.38.0 and GIMP 2.10.18 on Ubuntu 20.10.
Here's an upload on Imgur. Note that Imgur process the file making it larger however if you download it to check, and as seen below, the width=100 image shows white on Chromium 87:
It occurs to me you could make a progressive jpeg with only the DC coefficients, that a single grey pixel could be encoded in 119 bytes. This reads just fine in a few programs I've tried it in (Photoshop, GNOME Image Viewer 3.38.0, GIMP 2.10.18, and others).
ff d8 : SOI
ff db ; DQT
00 43
00
01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01
ff c2 ; SOF
00 0b
08 00 01 00 01 01 01 11 00
ff c4 ; DHT
00 14
00
01 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00
03
ff da ; SOS
00 08
01 01 00 00 00 01 3F
ff d9 ; EOI
The main space savings is to only have one Huffman table. Although this is slightly smaller than the 125 byte arithmetic encoding given in another answer, the arithmetic encoding without the JFIF header would be smaller yet (107 bytes), so that should still be considered the smallest known.
The above file can be generated with:
#!/usr/bin/env bash
printf '\xff\xd8' # SOI
printf '\xff\xdb' # DQT
printf '\x00\x43'
printf '\x00'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\x01\x01\x01\x01\x01\x01\x01\x01'
printf '\xff\xc2' # SOF
printf '\x00\x0b'
printf '\x08\x00\x01\x00\x01\x01\x01\x11\x00'
printf '\xff\xc4' # DHT
printf '\x00\x14'
printf '\x00'
printf '\x01\x00\x00\x00\x00\x00\x00\x00'
printf '\x00\x00\x00\x00\x00\x00\x00\x00'
printf '\x03'
printf '\xff\xda' # SOS
printf '\x00\x08'
printf '\x01\x01\x00\x00\x00\x01\x3F'
printf '\xff\xd9' # EOI