Sorry, no online dictionaries contain the exact phrase higher order.
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Reverse dictionary results:
1. higher up
 2. high level
3. higher criticism
4. higher education
5. above mentioned
6. uppermost
7. superior
8. advanced
9. hierarchical
10. upper limit
 11. hierarchically
12. hierarchy
13. increasing
14. overarching
15. highest
16. intellectual
17. intelligent
18. smarter
19. abovementioned
20. intelligence
 21. intellectuality
22. upper case
23. top level
24. complex
25. greater than
26. increased
27. loftier
28. intellectualized
29. upwards
30. hierarchal
 31. upwardly
32. greater
33. hierarch
34. intellectually
35. derivational
36. intellect
37. heightened
38. complexity
39. hierarchies
40. high minded

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You can look up the words in the phrase individually using these links:   higher ?   order ?
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