I'm currently performing a literature search to locate experimentally-verified fox deterrence methods - without much luck so far! But I've located several commercial products. Note that these may, or may not, be efficacious in deterring foxes! We'd have to test them in a controlled experiment to determine that.

Commercial products to deter foxes:

1. Foxlights use an array of small LED bulbs programmed to flash intermittently in random sequence over a 360-degree area and, with several positioned along a perimeter, are designed to mimic a person patrolling with a torch. 

2. "a device called a Scarecrow for fox deterrence. The Scarecrow is a water-jet triggered by an infrared sensor, sensitive to objects up to 11m (35ft) away – when triggered by movement it fires a three second jet of cold water from its sprinkler head. Mr Bryant explains that he has “found that it has deterred foxes that have defied all other repellents”" It was however noted that foxes habituated to this once they knew it was not harmful. It could also be dangerous in low temperatures to make the foxes wet! [2]

3. " Nite Eyes, consists of a series of flashing red LED lights and is reputed to deter a wide range of species, from owls to bears and cougars. The solar-powered device works by trying to fool the predator into thinking it’s being watched – the manufacturers note that “The sense of being watched is the greatest fear night animals have”. [2] Again, just off the top of head, I'd say habituation again might be an issue

4. Next we have ultrasonic devices, such as FoxWatch. "general idea being that they emit an ultrasonic sinus or siren-like sound -- which foxes find unpleasant -- every two seconds or so for a pre-set period after the device is activated .. those designed specifically to repel cats and dogs tend to operate at around 22 kHz". The red fox hearing range is  "60 dB sound pressure level (SPL) (re 20 μPa) red foxes perceive pure tones between 51 Hz and 48 kHz, spanning 9.84 octaves with a single peak sensitivity of -15 dB at 4 kHz" [1]

DISCUSSION

One study I've got so far per ultrasonic is for CatWatch. The abstract concludes "Results indicated that the device did have a moderate deterrent effect, reducing the probability of a cat intrusion into a garden by approximately 32% in the first experiment, but not in the second" [3]. I can't extrapolate this to foxes. The study however did mention that "Ultrasound deterrents for a variety of mammals, including cats, are widely available in the commercial market, but few have been independently tested for efficacy." 

According to [2]  "In their Unearthing the Urban Fox book, Trevor Williams and Andy Wilson describe how their own trials [ultrasonic] showed success rates of up to 80%, although they do not provide the details and Andy’s dissertation (conducted while he was a student at Greenwich University) wasn’t published – Mr Williams did tell me, however, that some of the companies weren’t happy with the findings of some of their tests. The Oxford Croquet club experienced problems with foxes digging and fouling their green and tried several repellents; on their website, they conclude:

“During experiments carried out in association with Greenwich University, we found ultrasonic devices broadly ineffective, but found a water driven gadget, called "Scarecrow", very effective.”

Of course, if it's unpublished it didn't pass peer review, so this is all kind of useless, besides giving us a 'feel' for the state of research.

Another study I've found is regarding badgers (yes, again, this can't be extrapolated to foxes). This study looked at ultrasonic, and water jets (as per Scarecrow commercial device mechanism). The conclusion being: "We conclude that neither device, used alone or in combination, present effective solutions to the growing problem of urban badger damage." " The ultrasonic device, whether used alone or in combination with the water jet, was associated with significantly higher badger activity at baited plots in comparison to control plots, and bait consumption was higher when the ultrasonic device was used alone." [4]

Another idea seems to be usage of radios to deter foxes - as a way of exposing them to auditory noxious stimuli of human voices

CONCLUSION

So we have mimic of torches being shined, spraying foxes with water jets, ultrasonic sounds @ 22kHz ish (well it's just plain sounds for foxes really, as their hearing range is to 48kHz!), human voice sounds (85-255Hz?), and mimic of predator eyes. And it seems there is very little published to validate any of these approaches experimentally!  

References:

[1]  A behavioral audiogram of the red fox (Vulpes vulpes). https://www.ncbi.nlm.nih.gov/pubmed/25529529

[2] http://www.wildlifeonline.me.uk/fox_deterrence.html

[3] The efficacy of an ultrasonic cat deterrent http://www.appliedanimalbehaviour.com/article/S0168-1591%2805%2900138-3/abstract

[4] Deterrent or dinner bell? Alteration of badger activity and feeding at baited plots using ultrasonic and water jet devices http://www.appliedanimalbehaviour.com/article/S0168-1591(08)00149-4/fulltext