MinT - Best Known (25−4, 25, s)-Nets in Base 4

Best Known (25−4, 25, s)-Nets in Base 4

Digital (21, 25, 4194301)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²⁵, 4194301, F₄, 4, 4) (dual of [(4194301, 4), 16777179, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4²⁵, 4194301, F₄, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(4²⁵, 8388602, F₄, 4) (dual of [8388602, 8388577, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²⁵, large, F₄, 4) (dual of [large, large−25, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]

Digital (21, 25, 7908855)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²⁵, 7908855, F₄, 4, 4) (dual of [(7908855, 4), 31635395, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4²⁵, 7908855, F₄, 3, 4) (dual of [(7908855, 3), 23726540, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4²⁵, 7908855, F₄, 4) (dual of [7908855, 7908830, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²⁵, large, F₄, 4) (dual of [large, large−25, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]

There is no (21, 25, large)-net in base 4, because