Perfect Pangram development

Question

I aim to craft very specific "perfect pangrams." A perfect pangram consists of exactly 26 letters, each used once. I include the letter lengths of each word, as well, between slashes \# #\:

• Bank Vext Quiz Cwms Fjord Glyph \4 4 4 4 5 5\

• Ox Qs Gyp Cwm Hadj Verb Link Futz \2 2 3 3 4 4 4 4\

• Ex Qs Zip Vug Cwm Nth Balky Fjord \2 2 3 3 3 3 5 5\

• Adz Jig Suq Pyx Cwm Nth Verb Folk \3 3 3 3 3 3 4 4\

• Qs Kaf Red Zig Job Luv Pyx Cwm Nth \2 3 3 3 3 3 3 3 3\

As you can see, many of the ones I've written are comprised of short words. What I'm hoping to uncover are very specific PP sets which include longer words:

• \3 3 5 5 5 5\

• \6 6 7 7\

• \5 5 8 8\

• \4 4 9 9\

As the words get longer, my expectation that they can be achieved drops, as there are only so many vowels (6) and vowelless, unique letter words to make up for it (Cwm Nth Pht Pst Tsk Cwms Crwth Crwths). Please use YAWL for the wordlist.

I've gotten close with each of these, but always have to include an additional word, leading to an imperfect pangram.

• Ave Mix Bop Quaky Fjeld Zings Crwth (MVP Box would've worked, had MVP not been an unaccepted initialism)

• Quartz Deluxe Blocky Vamping Jewfish

• Wharf Bring Quadplex Zemstvos Joystick

• Quad Wife Schmaltzy Depriving Jukeboxes

Answer 1

I found no pangrams for the requested '6 6 7 7' or '5 5 8 8' or '4 4 9 9'.
My answer for '3 3 5 5 5 5' using self-made code is

11 solutions:
fix lbw gecks jumpy tranq vozhd
gju pyx flick tranq vozhd wembs
gju vox blitz dreck nymph waqfs
jib pyx kreng mulct vozhd waqfs
jig pyx crumb knelt vozhd waqfs
jud vex brock glitz nymph waqfs
jug pyx flick tranq vozhd wembs
jug vox blitz dreck nymph waqfs
jun kex climb grypt vozhd waqfs
jut pyx climb kreng vozhd waqfs
pyx viz crwth fjeld gambs quonk

---

Update

I found 404838 perfect pangrams from the YAWL word list.
Here are some stats:

• YAWL has 264097 words, 48852 with unique letters, 36296 excluding anagrams
• Most anagrams: there are 13 anagrams of "alerts", "apers" and "arets"
• Most words: 9 such as "dzo fy gju hm lbw pranck qi st vex"
• Least words: 5 such as "goldbricks jynx putz vehm waqf"
• Longest word: "goldbricks", the only 10-letter word, appearing only once

I excluded anagrams until output, when each 'sentence' was permuted to cover them.
As you see, there are no four-word perfect pangrams.

I then rated each pangram according to the frequency that each of its words appears in the lists obtained from Keith Vertanen. The highest scoring pangram was

cwm fad jog lynx ph quiz tsk verb

so good luck with finding a nice perfect pangram!

The complete pangram list is available (for now) on Microsoft Onedrive.

Answer 2

Via integer linear programming (https://puzzling.stackexchange.com/a/123475/65277), here are the largest numbers of covered letters.

3 3 5 5 5 5

26:

{'blitz','dreck','gju','nymph','vox','waqfs'} {'blitz','dreck','jug','nymph','vox','waqfs'} {'flick','gju','pyx','tranq','vozhd','wembs'} {'brock','glitz','jud','nymph','vex','waqfs'} {'crumb','jig','knelt','pyx','vozhd','waqfs'} {'climb','jut','kreng','pyx','vozhd','waqfs'} {'climb','grypt','jun','kex','vozhd','waqfs'} {'crwth','fjeld','gambs','pyx','quonk','viz'} {'flick','jug','pyx','tranq','vozhd','wembs'} {'fix','gecks','jumpy','lbw','tranq','vozhd'} {'jib','kreng','mulct','pyx','vozhd','waqfs'}

6 6 7 7

25:

{'freckly','jawbox','tumping','vozhds'} {'flytrap','jumbuck','vozhds','wexing'}

5 5 8 8

25:

{'fumbling','pyrex','stickjaw','vozhd'} {'fumbling','prexy','stickjaw','vozhd'} {'flowback','jerquing','tymps','vozhd'} {'backflow','jerquing','tymps','vozhd'} {'jumbling','kvetched','proxy','waqfs'} {'fjord','vexingly','whipt','zambucks'} {'buckjump','flaxy','strewing','vozhd'} {'buckjump','flaxy','vozhd','wresting'} {'buckjump','flytings','rewax','vozhd'} {'buckjump','flytings','vozhd','waxer'} {'buckjump','swerf','taxingly','vozhd'}

4 4 9 9

25:

{'blackdamp','frowziest','jynx','vugh'} {'buckjumps','lynx','overdight','waqf'} {'drumbling','fozy','vext','whipjacks'} {'buckjumps','dragonfly','vext','whiz'}