Naively, we might count on a minRelayTxFee of 1000 sat/kb to correspond to 250 sat/kw. Nonetheless, apparently this isn’t so based on this concern (ACINQ), which additionally references this concern (c-lightning).

  /** 
    * why 253 and never 250 since feerate-per-kw is feerate-per-kb / 250 and the minimal relay price charge is 1000 satoshi/Kb ? 
    * 
    * as a result of bitcoin core makes use of neither the precise tx dimension in bytes or the tx weight to test charges, however a "digital dimension" 
    * which is (3 * weight) / 4 ... 
    * so we wish : 
    * price > 1000 * digital dimension 
    * feerate-per-kw * weight > 1000 * (3 * weight / 4) 
    * feerate_per-kw > 250 + 3000 / (4 * weight) 
    * with a conservative minimal weight of 400, we get a minimal feerate_per-kw of 253 
    * 
    * see https://github.com/ElementsProject/lightning/pull/1251 
    **/ 
   val MinimumFeeratePerKw = 253 ```

I assumed vbytes have been equal to weight models divided by Four and rounded up, so I do not perceive the place (3 * weight) / 4 comes from.