Here's that set of eliminations expressed as a MSLS which shows 8 lines and 1 box being covered.

98.7.....7.6...8......5....4......3..9.6.........24..1.6.9..5......3..4......1..2;38692;GP;12_07;1;1234; ; ;X; ;;

- Code: Select all
`Rows *-------------------------*-------------------------*-------------------------* Boxes`

56 | 9 8 12345 | 7 146 236 | 1234-6 1256 3456 | 1234 - -

59 | 7 12345 6 | 1234 149 239 | 8 1259 3459 | - . -

. | 123 1234 1234 | 12348 5 689-23 | 1234679 679-12 679-34 | - - .

*-------------------------*-------------------------*-------------------------*

. | 4 1257 12578 | 158 789-1 5789 | 267 3 5678 | . - -

578 | 123-58 9 123-578 | 6 178 3578 | 24-7 2578 4578 | - . -

. | 6 357 3578 | 358 2 4 | 79 5789 1 | - - .

*-------------------------*-------------------------*-------------------------*

78 | 123-8 6 1234-78 | 9 478 278 | 5 178 378 | . - -

. | 1258 1257 125789 | 258 3 5678-2 | 1679 4 6789 | - . -

. | 358 3457 345789 | 458 678-4 1 | 3679 6789 2 | - - .

*-------------------------*-------------------------*-------------------------*

Colms . . . . 14 23 . 12 34

Multi-sector Locked Set:(56)r1,(59)r2,(578)r5,(78)r7,(14)c5,(23)c6,(12)c8,(34)c9,(1234)b1 (21 cells/confined digits)

19 Eliminations in 12 cells.

A follow on step identifies (58)HS:r89c1 to make the cannibalistic eliminations given for the 2nd truth and link set approach. As these don't include (5)r89c2 this step is still needed, so the point about the extra eliminations is rather academic.

champagne, the collection of cover sets used has similarities with a single digit Franken Fish. As there are no columns covered in stack 1, any if its boxes can be added to cover the (1234) digit set. This may be of help for a redesign of your Multi-fish algorithm.

In the same way as for the truth & link set approach, the MSLS can be converted to its complement to give the same eliminations:

Multi-sector Locked Set:(1234)r3,(12)r4,(3)r6,(12)r8,(34)r9,(58)c4,(679)c7,(578)b4,(5789)b7 (23 cells/confined digits)

There is therefore still a free choice about whether to cover the focus digits by rows or columns.