I'll chime in a bit as well with my own experience with carrier operations as well since it looks like you are in a similar situation when I had to design my first carrier for my current game at what looks to be a similar tech level.
Note this is based off of V2.0X as I haven't dived into the newest version (still waiting to see if the new patch is coming out soon), but some things should still apply or can be adapted.
First, my carrier design and strike wing as comparison. I'll leave out the missiles as the mechanics have changed massively between versions. Also, the designs shown here are around 50 in-game years and 1.5 irl years behind from where my game save is currently, errors were discovered, corrected and newer designs were brought into service since.
Argus class Light Carrier 25,000 tons 356 Crew 2,792.5 BP TCS 500 TH 1,000 EM 0
2000 km/s Armour 3-76 Shields 0-0 HTK 124 Sensors 11/11/0/0 DCR 14 PPV 0
Maint Life 2.07 Years MSP 977 AFR 357% IFR 5.0% 1YR 304 5YR 4,553 Max Repair 125 MSP
Hangar Deck Capacity 12,000 tons Magazine 720
Captain Control Rating 3 BRG AUX ENG
Intended Deployment Time: 12 months Flight Crew Berths 240 Morale Check Required
Myerson & Micheli Ion Drive EP250.00 (4) Power 1000 Fuel Use 42.43% Signature 250 Explosion 10%
Fuel Capacity 2,061,000 Litres Range 35 billion km (202 days at full power)
Alamillo Weapon Systems CIWS-120 (2x8) Range 1000 km TS: 12,000 km/s ROF 5
Mk II-C Fighter ASM (360) Speed: 24,400 km/s End: 0.8m Range: 1.2m km WH: 5 Size: 2 TH: 162/97/48
Domeier-Kirch Warning & Control Active Search Sensor AS39-R100 (1) GPS 2100 Range 39.8m km Resolution 100
Domeier-Kirch Warning & Control EM Sensor EM1.0-11.0 (1) Sensitivity 11 Detect Sig Strength 1000: 26.2m km
Domeier-Kirch Warning & Control Thermal Sensor TH1.0-11.0 (1) Sensitivity 11 Detect Sig Strength 1000: 26.2m km
Strike Group
20x F-1C Eagle Fighter Speed: 12517 km/s Size: 4.99
24x FB-2D Viper Fighter-bomber Speed: 12546 km/s Size: 4.98
4x FS-3A Bat Fighter-Scout Speed: 12546 km/s Size: 4.98
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Military Vessel for maintenance purposes
This design is classed as a Carrier for auto-assignment purposes
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F-1C Eagle class Fighter 250 tons 2 Crew 53.5 BP TCS 5 TH 63 EM 0
12517 km/s Armour 3-3 Shields 0-0 HTK 2 Sensors 0/0/0/0 DCR 0 PPV 0.5
Maint Life 7.93 Years MSP 13 AFR 5% IFR 0.1% 1YR 0 5YR 6 Max Repair 31.25 MSP
Lieutenant Commander Control Rating 1
Intended Deployment Time: 7.1 days Morale Check Required
Myerson & Micheli Ion Drive EP62.50 (1) Power 62.5 Fuel Use 1325.83% Signature 62.5 Explosion 25%
Fuel Capacity 67,000 Litres Range 3.6 billion km (3 days at full power)
Delahoya-Youell Gauss Cannon R400-8.00 (1x4) Range 40,000km TS: 15,000 km/s Accuracy Modifier 8.00% RM 40,000 km ROF 5
Burin Electronic Systems Beam Fire Control R45-TS2000 (SW) (1) Max Range: 44,800 km TS: 2,000 km/s 39 28 17 5 0 0 0 0 0 0
This design is classed as a Fighter for production, combat and planetary interaction
This design is classed as a Fighter for auto-assignment purposes
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FB-2D Viper class Fighter-bomber 250 tons 2 Crew 52 BP TCS 5 TH 63 EM 0
12546 km/s Armour 3-3 Shields 0-0 HTK 2 Sensors 0/0/0/0 DCR 0 PPV 0.6
Maint Life 8.09 Years MSP 13 AFR 5% IFR 0.1% 1YR 0 5YR 5 Max Repair 31.25 MSP
Magazine 4
Lieutenant Commander Control Rating 1
Intended Deployment Time: 11.1 days Morale Check Required
Myerson & Micheli Ion Drive EP62.50 (1) Power 62.5 Fuel Use 1325.83% Signature 62.5 Explosion 25%
Fuel Capacity 56,000 Litres Range 3.05 billion km (67 hours at full power)
Size 2.0 Box Launcher (2) Missile Size: 2 Hangar Reload 70 minutes MF Reload 11 hours
Carullo-Huver Missile Fire Control FC16-R100 (1) Range 16.2m km Resolution 100
Mk II-C Fighter ASM (360) Speed: 24,400 km/s End: 0.8m Range: 1.2m km WH: 5 Size: 2 TH: 162/97/48
Wohlers-Reiley Active Search Sensor AS2-R1 (1) GPS 3 Range 2.3m km MCR 208.1k km Resolution 1
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Fighter for production, combat and planetary interaction
This design is classed as a Fighter for auto-assignment purposes
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FS-3A Bat class Fighter-Scout 250 tons 2 Crew 54.2 BP TCS 5 TH 63 EM 0
12546 km/s Armour 3-3 Shields 0-0 HTK 2 Sensors 1/1/0/0 DCR 0 PPV 0.3
Maint Life 8.69 Years MSP 13 AFR 5% IFR 0.1% 1YR 0 5YR 5 Max Repair 31.25 MSP
Magazine 2
Lieutenant Commander Control Rating 1
Intended Deployment Time: 7.1 days Morale Check Required
Myerson & Micheli Ion Drive EP62.50 (1) Power 62.5 Fuel Use 1325.83% Signature 62.5 Explosion 25%
Fuel Capacity 61,000 Litres Range 3.3 billion km (3 days at full power)
Size 2.0 Box Launcher (1) Missile Size: 2 Hangar Reload 70 minutes MF Reload 11 hours
Stengel Sensor Systems Missile Fire Control FC5-R1 (1) Range 5.4m km Resolution 1
Mk II-C Fighter ASM (1) Speed: 24,400 km/s End: 0.8m Range: 1.2m km WH: 5 Size: 2 TH: 162/97/48
Wohlers-Reiley Active Search Sensor AS2-R1 (1) GPS 3 Range 2.3m km MCR 208.1k km Resolution 1
Coltman Electronic Systems Thermal Sensor TH0.1-1.1 (1) Sensitivity 1.1 Detect Sig Strength 1000: 8.3m km
Coltman Electronic Systems EM Sensor EM0.1-1.1 (1) Sensitivity 1.1 Detect Sig Strength 1000: 8.3m km
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Fighter for production, combat and planetary interaction
This design is classed as a Fighter for auto-assignment purposes
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Now diving right in, I saw my fighter wings doing two separate things, the beam fighters acting as interceptors against enemy attacks, escorts for my fighter bombers and finally finishing off any crippled enemy ships. The bombers were there to deliver ranged attacks against enemy ships and perform long range missile defense if necessary. The armor on the fighters was intended to make it harder for any 10cm laser equipped escorts from one-shotting my fighters at close range and allowed the testing of the power and range of the weapons on unknown classes.
I saw the carriers themselves as belonging nowhere near combat and was (and still am) willing to sacrifice my fighters to keep the carrier safe from harm. The 3b km range of my fighters allow my carrier to launch from well outside the known sensor range of my enemy ships and be able to throw in a dogleg into any inbound or outbound strikes for further obscuring of the fighter origins.
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If we use my carrier as a basis, then it can have two squadrons of 20 (total 40) of your bombers with four of your scout aircraft, allowing an increase of 28 bombers and 2 scouts. An alternative is to modify my fighter-bomber to carry 1 Size-8 box launcher (dropping Armor to 1 and replacing the Size-2 box launchers) instead of your bombers. This cuts down on the number of missiles from 80 to 40 but is still greater than the 32 that your wing can throw from your carrier.
Modifications done to my carrier can be done to raise its speed. Dropping the CIWS (useless in 2.51), some fuel, and the hanger bay to 9000 tons allows the doubling of engine space and using 1500 ep, 150% boosted ion engines allow the new design to go at 6000 km/s while still having a range of over 20b km and able to carry 32 bombers and 2 scouts.
Using your bomber, you will have a larger strike wing while also retaining some speed and have a greater cruising range using this design while switching over to my modified fighter allows you to have the same number of missiles able to be launched farther from the carrier but at the cost of doubling the craft (and associated costs) to do so.
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An alternative to the above suggestions is to have a small fighter tanker assigned as part of the carrier wing. Below is my first such design. I need multiple of these for my fighter operations, but a single tanker can double your fighter strike range if you can preposition it. You would need to drop one of the scouts or two of your bombers to carry the tanker in your carrier.
K-1A Dove class Strike Craft Tanker 500 tons 4 Crew 45.4 BP TCS 10 TH 40 EM 0
4002 km/s Armour 1-5 Shields 0-0 HTK 3 Sensors 1/1/0/0 DCR 0 PPV 0
Maint Life 2.59 Years MSP 5 AFR 20% IFR 0.3% 1YR 1 5YR 16 Max Repair 20 MSP
Lieutenant Commander Control Rating 1
Intended Deployment Time: 1 months Morale Check Required
Wolsey Aero Engines Magnetic Fusion Drive EP40.00 (1) Power 40 Fuel Use 67.08% Signature 40 Explosion 10%
Fuel Capacity 301,000 Litres Range 161.6 billion km (467 days at full power)
Refuelling Capability: 10,000 litres per hour Complete Refuel 30 hours
Hendershott-Dorsch Sensor Systems Active Search Sensor AS16-R100 (1) GPS 280 Range 16.4m km Resolution 100
Asta Electronic Systems Thermal Sensor TH0.1-1.4 (1) Sensitivity 1.4 Detect Sig Strength 1000: 9.4m km
Gitto Warning & Control EM Sensor EM0.1-1.4 (1) Sensitivity 1.4 Detect Sig Strength 1000: 9.4m km
This design is classed as a Fighter for production, combat and planetary interaction
This design is classed as a None for auto-assignment purposes
Checking the math, a modified version of the tanker is able to fully refuel a 16 strong strike of your bombers out of its reserves and still have 13b km in range if using a 60ep, 240% boosted ion engine while pushing the tanker up to 6000k km/s. It would take over 20 hours to finish refueling your fighters, but it is an option for a long-range strike.