MinT - Information on Result #1758540

Information on Result #1758540

Digital (224, 241, 2102611)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴¹, 2102611, F₂, 4, 17) (dual of [(2102611, 4), 8410203, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵⁶, 5461, F₂, 4, 8) (dual of [(5461, 4), 21788, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁵⁶, 5461, F₂, 3, 8) (dual of [(5461, 3), 16327, 9]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2⁵⁶, 16383, F₂, 8) (dual of [16383, 16327, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁵⁶, 16384, F₂, 8) (dual of [16384, 16328, 9]-code), using
        1 times truncation [i] based on linear OA(2⁵⁷, 16385, F₂, 9) (dual of [16385, 16328, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
2. linear OOA(2¹⁸⁵, 2097150, F₂, 4, 17) (dual of [(2097150, 4), 8388415, 18]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.