MinT - Best Known (19, 19+4, s)-Nets in Base 4

Best Known (19, 19+4, s)-Nets in Base 4

Digital (19, 23, 1398101)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²³, 1398101, F₄, 4, 4) (dual of [(1398101, 4), 5592381, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4²³, 1398101, F₄, 3, 4) (dual of [(1398101, 3), 4194280, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(4²³, 2796202, F₄, 4) (dual of [2796202, 2796179, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²³, 2796203, F₄, 4) (dual of [2796203, 2796180, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]

Digital (19, 23, 1977213)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²³, 1977213, F₄, 4, 4) (dual of [(1977213, 4), 7908829, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4²³, 1977213, F₄, 3, 4) (dual of [(1977213, 3), 5931616, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4²³, 1977213, F₄, 4) (dual of [1977213, 1977190, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²³, 2796203, F₄, 4) (dual of [2796203, 2796180, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]

There is no (19, 23, 3954427)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 70 368759 563965 > 4²³ [i]