Can the DNL error of ADC be less than in negative more than 1LSB
Can DNL be  than &lt;-1 ? (worse)


Yes it's possible, yet I don't know any off hand. 

Perhaps with conduction crosstalk between digital and analog ground it's possible or in an embedded uC from the digital channel. However, that could be an error to spec or an EMC layout issue.  They take great care to design and isolate these incompatible processes of precision Analog and high speed digital. But it's better to keep them honest. Trust but verify.

The differential nonlinearity (DNL) error reveals how far a code is from a neighbouring code in a ramped analog input test.  It is normally &lt;+/-1 bit which is monotonic but could be +/-1 bit which may slip 1 code unless guaranteed otherwise.

+/-2 bits or more might be possible if it were an extremely low resolution like 24 bits. THese would be laser trimmed parts to achieve the specs, but it's possible digital noise currents in a bad layout could shift the analog ground for Vref in the ADC.

My 1st design with an ADC in 1976 which used the best ADC by Burr-Brown (now TI) a 12 bit high-speed TTL ceramic Hybrid with Mil-Std-883 class rated part for a critical reliability application. Fortunately, I discovered missing codes with my custom linearity triangle wave tests, generated by a triangle wave input to ADC hen output to a similar BB DAC and compare both on a scope in AC coupled mode looking for a non-single step.   I had spare parts worth $1xx each and both had the many missing code errors right near major data transitions  like ...xxx1000 to ...xxx0111.  When BB did not give me a satisfactory explanation. I order the Industrial lower grade equivalent version.  They were all faultless!  I concluded they had a process/design flaw in this version between TTL logic current and Vref ground that caused this apparent hysteresis of a missing codes in several places that was not picked up by X-RAY pre-cap inspection or functional test. I even began to suspect the X-RAY induced the failure, which is why I ordered the non MIL-spec replacement. My hunch worked, maybe by coincidence.

But I were you, I would design a self-test to verify linearity or at least an easy test for any new design. It's not hard.