The design uses a tuning capacitance that is lower than 160pF. The coil must be designed to provide the necessary inductance in order for resonance to occur. I understand that you added capacitance to get to 3.8nF because this is the value necessary to resonate with 32uH. However, the literature including the referenced website and the datasheet for the MK484 (
http://www.datasheetcatalog.org/datasheet/RECTRON/MK484.pdf ) all say that the inductor, when wound correctly, will resonate with capacitance of less than 160 pF. This implies that the inductance should be around 530 uH. I think that you are calculating the inductance of your inductor incorrectly. To construct the inductor, you wind the litz wire around the ferrite bar. The ferrite bar is the core of the inductor. When you wind wire on a ferrite bar, the ferrite magnifies the inductance a great deal, so you cannot use a formula for an air core coil to calculate the value of this one. Also, ferrite bars are different depending on its size and its composition, so the chances are good that you don't know the exact amount by which the ferrite will magnify the inductance. For this reason, I recommend that you figure out how to measure the inductance of your coil. These are some methods:
- find someone with an inductance meter and measure your coil with it
or
- wire your inductance in parallel with a ceramic capacitor of known value, for example a 150 pF ceramic cap and then couple an AC voltage into it. Vary the AC voltage to find the point where the tank voltage is at a peak
(if you can borrow a "grid dip meter" or "gate dip meter" (a useful instrument used by Hams to measure resonance of tank circuits) use that to measure the coil resonant frequency). this can be tricky for someone with no tools or instruments but it can be done. Do you have any instruments such as a function generator or an oscilloscope?
or
build a simple inductance meter yourself. its not complicated unless you have no meters or instruments of any kind.
or
wire your inductor in parallel with a variable capacitor. Place the inductor ferrite bar very close to the antenna of an AM receiver and tune the AM receiver to a weak station. Then adjust your variable capacitor to see if, while you are adjusting the capacitor you find any spot where the sound from your AM receiver gets a lot louder. If this happens, your ferrite plus variable cap is resonating at the receiver frequency.
Another approach is to assume that your inductor is fairly close, but not right on. Change your capacitance to only have the variable capacitor of less than 200 or 300 pF and leave out the rest of the capacitors. Then tune the capacitor to see if there is a point where you hear your bug very strongly.
edit: I found a couple of AM radio antennas here in my junk box and measured the inductance. I get 700 uH for one and 745uH for another. The one with 700uH is typical of an AM antenna inside a portable AM radio, in that the ferrite bar is 55mm long and it has about 80 to 100 turns of wire on it. In addition, I also have the windings from an AM bar antenna that have slipped off their bar, essentially just an air core coil. So I measured that air core coil and get 70uH. Then I slipped that coil onto a ferrite bar. The inductance increased to 745 uH. This coil is approximately 100 turns of 3 cond litz wire, with diameter of roughly 11mm. This is roughly like yours, I think. So as you can see, the ferrite magnifies the inductance by a lot, about 10 times in my case. Perhaps you could assume that your inductor is around 550 uH. Such a coil would resonate at 457 KHz with a 220pF ceramic capacitor, or with your 160pF variable (set about halfway) in parallel with another 150pF fixed ceramic cap.