Which box for JBL 2042HPL

Tell me which box can be built for them, do I prefer a transmission line or a Back Horn.
Greets!

Hmm, upper mass corner (Fhm) = 2*Fs/Qes* = ~71.0/86.5 Hz = BLH IME or even the simple BIB variant, though due to either's size, maybe best overall just a damped/stuffed to 'taste' floor loaded TL or inverted BIB.

* using this as an approximation of Qts + some series resistance due to VC heating.
 
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Both Bl roducts (10.876 Tm and 11.625 Tm, from post #16) are not weak by today standards - they are the same as any modern low-cost 15-inch woofers, like GRS or Goldwood. Relatively low Bl product is not the (direct) problem - it is the high Qts parameter (which depends on Bl value, of course), which excludes bass-reflex boxes. Both woofers from post #16 will work OK only in the closed or aperiodic box.
I am not familiar with your description "1970's design box" - what does it mean? In the seventies speakers boxes generally were big - if that is what you want to say. Bur some modern/contemporary speakers are even bigger, especially if they contain 15-inch woofer.